Sequences and series questions | form three Basic Mathematics

How many terms of the series 3 + 6 + 9 + 12 + . . . are needed for the sum to be 630?

The sum of the first three terms of a G.P is 13. Find the sum of the first five terms if the common ratio of the G.P is

1. Exaplain with examples the relationship between sequence and series.
2. Show that the sum of the first n natural numbers is given by the formula
3. By using the formula in (b) above calculate the sum of the first 100 natural numbers.

Identify whether the series 5+10+20+…. is an arithmetic progression or a geometric progression and hence find ;

1. The sum of the 8^th , 9^th and 11^th terms
2. The value of n for which the n ^th term is 2560

(a) If the sum of n terms of a geometric progression with first term 1 and common ratio   is  , find the number of terms.
(b) How many integers are there between 14 and 1,000 which are divisible by 17?

The 8^th term of an arithmetic progression is 9 greater than the 5^th term and the 10^th term is 10 times the 2^nd term.Find the common difference and the first term of an arithmetic progression.

The sum of the first two terms of a geometric progression is 18 whereas the sum of the second and the third term is 54, find the first term and the common ratio.

The 20^th  term of an arithmetic progression is 60 and the 16^th  term is 20 . Find the sum of the first 40 terms.

The first term of an arithmetic progression is 12 and the common difference is 10. Find the n ^th  term.

If the 5^th  term of an arithmetic progression is 23 and the 12^th  term is 37, find the first term and the common  difference.