Question

In a geometric progression, the 5th term is 16 times the first term. Find the 7th term if the first term is 2

• A. 128
• B. 256
• C. 512
• D. 1024

Answer 1

Answer:

A. 128

$nth term =a(r-1)^n/(r-1)$

$first term (a)= 2$

$5th term = a(r-1)^5/(r-1)=16a$

$\frac{2(r-1)^5}{r-1}=16\times2$

$(r-1)^4=16$

$(r-1)^4=2^4$

$r-1=2$

$r=2+1=3$

$7th term = a(r-1)^7/(r-1)$

$=\frac{2(3-1)^7}{(3-1)}$

$=\frac{2\times2^7}{2}$

$=128$