Sequences and series questions | form three Basic Mathematics

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.

Answer / Solution

UNSOLVED

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.

Answer / Solution

UNSOLVED

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.

Answer / Solution

UNSOLVED

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.

Answer / Solution

UNSOLVED

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

Answer / Solution

UNSOLVED