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Form 3 Questions and Answers on Sequence and Series
Find the sum of the first 30 terms of the series:
16+19+22+……
(2m 44s)
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1.
The average of the first and the fourth term of a GP is 140.Given that the first term is 64, find the common ratio.
2.
A machine starts production of matchboxes at the rate of 12,000 per hour.The rate of production decreases by 40% every hour. Calculate the total number of matchboxes produced in the first two hours.
3.
The first, the third, and the seventh term of an increasing arithmetic progression are three consecutive terms of a geometric progression. If the first term of the arithmetic progression is 10,find the common difference of the arithmetic progression .
4.
The second and fifth terms of a geometric progression are 16 and 2 respectively. Determine the common ratio and the first term.
5.
Kubai saved sh.2,000 during the first year of employment.In each subsequent year,he saved 15% more than the preceeding year until he retired. (a) How much did he save in the second year? (b) How much did he save in the third year? (c) Find the common ratio. (d) How many years did he take to save a sum of sh.58,000? (e) How much had he saved after 20 years of service?
6.
In a geometric progression, the first term is a and the common ratio is r. The sum of the first two terms is 12 and the third terms is 16. (a) Determine the ratio #frac{ar^2} {a + ar}# (b) If the first term is larger than the second term,find the value of r.
7.
A colony of insect was found to have 250 insect at the beginning. Thereafter the number of insects doubled every 2 days.Find how many insects were there after 16 days.
8.
The first three consecutive terms of a geometrical progression are 3,x and #5 1/3#.Find the value of x.
9.
Abdi and Amoit were employed at the beginning of the same year. Their annual salaries, in shillings progressed as follows: Abdi: 60 000, 64 800, 69 600,…. Amoit: 60 000, 64 800, 69 984,…. (a) Calculate Abdi’s annual salary increment and hence write down an expression for his annual salary in his #n^(th# year of employment. (b) Calculate Amoit’s annual percentage rate of salary increment and hence
10.
The product of the first three terms of a geometric progression is 64.If the first term is a and common ratio is r. (a) Express r in terms of a. (b) Given that the sum of the three terms is 14 (i) Find the values of a and r and hence write down two possible sequences each upto #4^(th# term. (ii) Find the product of the# 50^(th# terms of the two sequences.
11.
(a) The first term of arithmetic progression (AP) is 2.The sum of the first 8 terms of the AP is 156. (i) Find the common difference of the AP. (ii) Given that the sum of the first n terms of the AP is 416,find n. (b) The #3^(rd#,#5^(th# and #8th# terms of another AP from the first three terms of a geometric progression (GP).If the common difference of the AP is 3,find (i)the first term of the GP
12.
The first,fifth and seventh terms of an arithmetic progression (AP) correspond to the first three consecutive terms of a decreasing Geometric Progression (GP).The first term of each progression is 64,the common difference of the AP is d and the common ratio of the GP is r. (a)(i) Write two equations involving d and r. (ii) Find the values of d and r (b) Find the sum of the first 10 terms of:
13.
Amana was paid an initial salary of ksh 180,000 per annum with a fixed annual increment.Bundi was paid an initial salary of ksh150,000per annum with 10% increment compounded annually. (a) Given that Amana’s annual salary in the #11^(th# year was ksh 288,000,determine: (i) His annual increment (ii) The total amount of money Amaya earned during the 11 years. (b) Determine Bundi’s monthly earnings
14.
In a jua kali factory,the number of pans produced in the first month is 250.The number of pans produced per month increases on the average by 30.Find the expected number of pans produced for the first 12 months.
15.
Find the sum of the first 30 terms of the series: 16+19+22+……
16.
A man deposited his money in a savings bank on a monthly basis. Each deposits exceeds the previous one by sh.750.If he started by depositing sh 1,500 how much will he have deposited in 12 months?
17.
Onyango and Kamau were employed on the same day and their salaries were as follows: Onyango: sh.11,000 per month and an increment of sh.300 at the end of every year. Kamau: sh.10,000 per month and an increment of sh.500 at the of every year.After how many years will they earn equal salaries.
18.
An employee started on a salary of ksh 6,000 per annum and received a constant annual increment.If he earned a total of ksh 32,400 by the end of five years,calculate his annual increment.
19.
An arithmetic progression has the first term a and common difference d. (a) Write down the third,ninth and the twenty fifth terms of the progression. (b) The arithmetic progression above is such that it is increasing and that the third, ninth and the twenty fifth terms form the first three consecutive terms of a geometric progression .The sum of the seventh and twice the sixth terms of the
20.
The third and fifth term of an Arithmetic Progression are 10 and -10 respectively. (a)Determine the first term and common difference. (b)The sum of the 15 terms.
21.
(a) The first term of an arithmetic progression is 4 and the last term is 20.The sum of the terms is 252. Calculate the number of terms and the common difference of the arithmetic progression. (b) An experimental culture has an initial population of 50 bacteria. The population increased by 80% every 20 minutes. Determine the time it will take to have a population of 1.2 million bacteria.
22.
The eleventh term of an arithmetic progression is four times its second term. The sum of the first seven terms of the same progression is 175. (a) Find the first term and common difference of the progression. (b) Given that the #p^(th# term of the progression is greater than 124,find the least value of
23.
The #n^(th# term of a sequence is given by 2n+3 (a) Write down the first four terms of the sequence. (b) Find S
50
,the sum of the first fifty terms of the sequence. (c) Show that the sum of the first n terms of the sequence is given by Sn=n2+4n.Hence or otherwise find the largest integral value of n such that Sn<725
24.
Each month, for 40 months, Amina deposited some money in a saving scheme. In the first month she deposited sh.500. Thereafter she increased her deposit by sh.50 every month. Calculate the: (a) Last amount deposited by Amina b).Total amount Amina had saved in the 40 months
25.
Find the number of terms of the series 2+6+10+14+18+…..that will give sum of 800.
26.
A carpenter wishes to make a ladder with 15 cross-pieces. The cross-pieces are to diminish uniformly in lengths from 67 cm at the bottom to 32 cm at the top. Calculate the length ,in cm of the seventh cross-piece from the bottom.
27.
The first term of an arithmetic progression (A.P) with six terms is p and its common difference is c. Another A.P with five terms has also its first term as p and a common difference of d.The last terms of the two Arithmetic Progression are equal . (a) Express d in terms of c. (b) Given that the 4th term of the second A.P exceeds the 4th term of the first one by 112,find the values of c and d.
28.
The sum of n terms of sequence:3,9,15,21….. is 7500.Determine the value of n.
29.
The first term of an arithmetic sequence is -7 and common difference is 3. (a) List the first six terms of the sequence. (b) Determine the sum of the first 50 terms of the sequence.
30.
Mute cycled to raise fund for charitable organization .On the first day ,he cycled 40km.For the first 10 days ,he cycled 3 km less on each subsequent day.Thereafter ,he cycled 2km less on each subsequent day. (a) Calculate: (i)the distance cycle on #10^(th# day (ii)the distance cycled on the #16^(th# (b) If mute raised ksh 200 per km, calculate the amount of money collected.
31.
The 5th term of an AP is 82 and the 12th term is 103. Find: (i)the first term and common difference (ii)the sum of the first 21 terms. (b) A staircase was built such that each subsequent stair has a uniform difference in height.The height of the 6th stair from the horizontal floor was 85 cm and the height of the 10th stair was 145 cm.Calculate the height of the 1st and the uniform difference in
32.
The #5^(th# and #10^(th# terms of an arithmetic progression are 18 and -2 respectively. (a) Find the common difference and the first term. (b) Determine the least number of terms which must be added together so that the sum of the progression is negative .Hence find the sum.
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