Now let us learn how to construct a GP. when the first term ‘a’ and common ratio ‘r’ are
given. And also learn how to check whether the given list of numbers is a GP.
Example-16. Write the GP. if the first term a = 3, and the common ratio r = 2.
Solution : Since ‘a’ is the first term it can easily be written
We know that in GP. every succeeding term is obtained by multiplying the preceding
term with common ratio ‘r’.
So to get the second term we have to multiply the first term a = 3
by the common ratio r = 2.
\ Second term = ar = 3 × 2 = 6 (Q First term × common ratio)
Similarly the third term = second term × common ratio
= 6 × 2 = 12
If we proceed in this way we get the following G.P.
3, 6, 12, 24,..... .
Example-17. Write GP. if a = 256, r =
1/
2
-
Solution : General form of GP =
Example-18. Find the common ratio of the GP 25, -5, 1,-5/1 Solution : We know that if the first, second, third .... terms of a GP are
Example-19. Which of the following lists of numbers form GP?
(i) 3, 6, 12, ..... (ii) 64, -32, 16,
(iii)
1 11
, , ,......
Example-19.