a) An arithmetic progression is such that the first term is 5, the last is 135 and the sum of progression is 975.
i) The number of terms in the series (7mks)ii) The common difference of the progression (2mks)b) The sum of the first three terms of a geometric progression is 27 and the first term is 36. determine the common ratio and the value of the fourth term (4mks)
Worked Solution:
Form 3 Mathematics
The 5th and 10th 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. Form 3 MathematicsThe first three consecutive terms of a geometrical progression are 3, x and 5 ^{1}/_{3}. Find the value of x. ( 2 marks) Form 3 Mathematics
(a) The 5th term of an AP is 82 and the 12th term is 103.
Find: (i) the first term and the 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 stair and the uniform difference in height of the stairs. Form 3 Mathematics
The first, fifth and seventh terms of an arithmetic progression (AP) correspond to the first three consecutive terms of a decreasing Geometric Progression (G.P.)
The first term of each progression, is 64, the common difference of the AP is d and the common ratio of the G.P. is r a i) Write two equation involving d and r ii) Find the values of d and r (4 mks) b) Find the sum of the first 10 terms of i) The arithmetic progression(A.P); ii)The Geometric Progression (G.P) Form 3 Mathematics
The first term of an arithmetic sequence is — 7 and the common difference in 3
(a) List the first six terms of the sequence; (b) Determine the sum of the first 50 terms of the sequence. Form 3 Mathematics
Find the number of terms of the series 2 + 6 + 10 + 14 + 18 + ……….. that will give a sum of 800.
Form 3 Mathematics
Mute cycled to raise funds for a charitable organisation. On the first day, he cycled 40 km. 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 cycled on the 10th day ii)The distance cycled on the 16th day b) If Mute raised kshs 200 per km, calculate the amount of money collected Form 3 Mathematics
The first term of an arithmetic sequence is — 7 and the 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. Form 3 Mathematics
A colony of insects was found to have 250 insects at the beginning. Thereafter the number of insects doubled every 2 days. Find how many insects there were after 16 days. (3 mks)
Form 3 Mathematics
The sum of n terms of the sequence; 3, 9, 15, 21, … is 7500. Determine the value of n
Form 3 Mathematics
The first, fifth and seventh terms of an Arithmetic Progression (AP) correspond to the first three consecutive terms of a decreasing Geometric Progression (G.P).
The first term of each progression is 64, the common difference of the AP is d and the common ratio of the G.P 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: (i) The Arithmetic Progression (A.P); (ii) The Geometric Progression (G.P). Form 3 Mathematics
The first term of an Arithmetic Progression (A.P.) with six terms is p and its common difference is c. Another AP. with five terms has also its first term asp and a common difference of d. The last terms of the two Arithmetic Progressions 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 1, find the values of e and d. (c) Calculate the value of p if the sum of the terms of the first A.P. is 10 more than the sum of the terms of the second A.P. Form 3 Mathematics
a)The first term of an 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 3rd, 5th and 8th terms of another AP form 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; ii) The sum of the first 9 terms of the GP, to 4 significant figures. Form 3 Mathematics
The product of the first three terms of geometric progression is 64. If the first term is a, and the common ration is r.
(a) Express r in terms of a (b) Given that the sum of the three terms is 14 (i) Find the value of a and r and hence write down two possible sequence each up to the 4^{th} term. (ii) Find the product of the 50^{th} terms of two sequences 
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