Sequence And Series Question 290
Question: If three geometric means be inserted between 2 and 32, then the third geometric mean will be
Options:
A) 8
B) 4
C) 16
D) 12
Show Answer
Answer:
Correct Answer: C
Solution:
$ 2,,g_1,\ g_2,\ g_3,\ 32 $ where $ a=2,\ ar=g_1,\ ar^{2}=g_2,\ ar^{3}=g_3 $ and $ ar^{4}=32 $ Now $ 2\times r^{4}=32\Rightarrow r^{4}=16={{(2)}^{4}}\Rightarrow r=2 $ . Then third geometric mean $ =ar^{3}=2\times 2^{3}=16 $ . Aliter : By formula, $ G_3=2.{{( \frac{32}{2} )}^{3/4}}=2\ .\ 8=16 $ .
BETA
