Sequences and series questions | form three Basic Mathematics

(a) If the first term of an arithmetic progression is 3 and the third term is 13, find the second term, the fourth term and the sum of the first ten terms.
(b) A certain geometric progression has a common ratio of 2 and the sum of the first five terms is 155. Find the first term and give the formula for the n ^th  term.

1. Find the general term and hence the 30^th term of the sequence 1, -2, 4, -8,……
2. Given the series 100+92+84+…..

Find

1. The 20^th term
2. The sum of the first 20 terms.

Write down the next two terms in the sequence ,

1. The n ^th term of an AP is 12-4n. Find the first term and the common difference
2. In an AP the 1^st term is -10 , the 15^th term is 11 and the last term is 41. Find the sum of all the terms in the progression.

The 5^th term of a GP is 8, the third term is 4 and the sum of the first ten terms is positive. Find the first term, the common ratio and the sum of the first ten terms.

The first four terms of an AP are 2, (a-b) , (2a+b+7) and (a-3b) respectively where a and b are constants.

1. Find the value of constants a and b
2. The sum of the first 10 terms.

The 4^th , 6^th  and 9^th  terms of an arithmetical progression (A.P.) forms the first three terms of a geometric progression. If the first term of the A.P. is 3, determine the

1. Common difference of the arithmetical progression.
2. Common ratio of the geometrical progression.

The sum of the first six terms of an AP is 72 and the second term is seven times the fifth term.
(i) Find the first term and the common difference.
(ii) Find the sum of the first ten terms.

1. Compute the sum of the first ten terms of the series 1 + 5 + 9 + .…
2. The 5^th  term of an arithmetic progression is 23 and the 12^th  term is 37.

Find

1. the eleventh term
2. the sum of the first eleven terms by using the values computed in (b)(i) above without using the common difference for this progression.

The second, fifth and eleventh terms of an arithmetical progression are in geometrical progression, and
the seventh term is 4. Find

1. the common ratio of the geometrical progression
2. the common difference of the arithmetical progression