If the 4th and 7th terms of a GP are 250 and 31250 respectively. Find the two possible values of a and r

a = 2, r = 5

Step-by-step explanation:

Nth term of a GP = a*r^ (n-1)

Where 'a' is the first term and 'r' is the common ratio

4th term = a*r^3 = 250

r^3 = 250/a

7th term = a*r^6 = 31250

a*r^6 = 31250

a * (r^3) ^2 = 31250

a * (250/a) ^2 = 31250

a * (62500/a^2) = 31250

62500/a = 31250

a = 62500/31250 = 2

a = 2

since r^3 = 250/a,

r^3 = 250/2 = 125

r = (125) ^ (1/3)

r = 5