Question

If the 4th and 7th terms of a G.P. are 24 and 192 respectively , find the sum of 5 terms of this G.P. ​

Answer 1

Answer:

93

Step-by-step explanation:

Tn = ar^(n-1)

T7 = ar^(7-1) = ar^6

T4 = ar^(4-1) = ar^3

T7/T4 = ar^6/ar^3

192/24 = r^3

8 = r^3

r = 2 (cube root of 8 = 2)

T4 = ar^3

24 = a(2^3)

24 = 8a

a = 24/8

a = 3

Sum of first five terms

Sn = a(r^n - 1)/(r-1)

Sn = 3(2^5 - 1)/(2-1)

Sn = 3(32 - 1)/1

Sn = 3(31)

Sn = 93