Arithmetic & Geometric Progressions (CIE IGCSE 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]

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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.