Arithmetic & Geometric Progressions (Cambridge O Level Additional Maths)

In an arithmetic progression, the th term is equal to of the th term. The sum of the th term and the th term is equal to .

Find the sum of the first  terms of this progression.

In a geometric progression, the sum of the first two terms is equal to . The sum to infinity is equal to .
Find the possible values of the first term.

The sum of the first two terms of a geometric progression is 10 and the third term is 9.

In an arithmetic progression,  and . Find  the sum of the 100th to the 200th terms of the progression.

An arithmetic progression has a second term of -14 and a sum to 21 terms of 84. Find the first term and the 21st term of this progression.

A geometric progression has a second term of  and a fifth term of  . The common ratio,, is such that .

Find  in terms of . 

Hence find, in terms of , the sum to infinity of the progression. 

Given that the sum to infinity is 81, find the value of .

The first 5 terms of a sequence are given below.

4    -2    1    -0.5    0.25

[2]

[2]

The tenth term of an arithmetic progression is 15 times the second term. The sum of the first 6 terms of the progression is 87.

[4]

For this progression, the  term is 6990. Find the value of .

[3]

An arithmetic progression has a first term of 7 and a common difference of 0.4. Find the least number of terms so that the sum of the progression is greater than 300.

The sum of the first two terms of a geometric progression is 9 and its sum to infinity is 36. Given that the terms of the progression are positive, find the common ratio.

An arithmetic progression has a second term of 8 and a fourth term of 18. Find the least number of terms for which the sum of this progression is greater than 1560.

A geometric progression has a sum to infinity of 72. The sum of the first 3 terms of this progression is .

[5]

[1]

A geometric progression has a first term of 3 and a second term of 2.4. For this progression, find the sum of the first 8 terms.

Find the sum to infinity.

Find the least number of terms for which the sum is greater than 95% of the sum to infinity.

The 2nd, 8th and 44th terms of an arithmetic progression form the first three terms of a geometric progression. In the arithmetic progression, the first term is 1 and the common difference is positive.