Question

In a GP 3rd term is 24 and 6th term is 192. Find the tenth term:

• A. 6144
• B. 3072
• C. 2048
• D. 1536

Answer 1

Answer:

B. 3072

$a_3=24,a_6=192$

$a_n=ar^{(n-1)}$

$a_3=24=ar^2....(1)$

$a_6=192=ar^5...(2)$

$(2)/(1)\implies$

$\frac{ar^5}{ar^2}=\frac{192}{24}$

$r^3=8$

$r=2$

$(1)\implies{ar^2}=a\times2^2=24$

$a=24/4=6$

$a_{10}=6\times2^{(10-1)}$

$=6\times2^9=3072$