if the 2th and 4th term of a gp are 8 and 32 respectively. find the sum of the first 9th term

Answer 1

If the second and fourth terms of Geometric Progression (GP) is 8 and 32, it means they are two terms apart (4–2 = 2).

Since GPs follow the standard rule of multiplying the previous term by a fixed integer to get the subsequent term and that 8 and 32 are two terms apart, we simply have to find the quotient of 8 and 32 to the ratio of terms moved.

32/8 = 4 of which 4/2 terms = 2.

Therefore, the GP will be as follows 4, 8, 16, 32

The sum would then be 4 + 8 + 16 + 32 = 60

Answer 2

Using the familiar formulas you have been given:
"the 2th and 4th term of a gp are 8 and 32" ---> ar = 8 , ar^3 = 32
divide one equation by the other:
ar^3 / (ar) = 32/8
r^2 = 4
r = ± 2
if r = 2, a(2) = 8 ----> a = 4
if r = -2, a = -4

sum(9) = a(r^9 - 1)/(r-1)

for a=4,r=2 , Sum(9) = 4(2^9 -1)/1 = 2044
for a=-4, r = -2 , Sum(9) = -4((-2)^9 - 1)/(-2-1) = -684