Question

Insert five arithmetic means between 20 and 32.

• A.
  $22,24,26,28,30$
• B.
  $34,36,38,40,42$
• C.
  $42,44,46,48,50$
• D.
  $52,54,56,58,60$

Answer 1

The correct option is A

$22,24,26,28,30$
Let $A_1,A_2,A_3,A_{4}and{A}_5$ be five arithmetic means between 20 and 32.

$\therefore 20,A_1,A_2,A_3,A_4,A_5,32areinA.P.\text{Last term}=32\Rightarrow a+(n-1)d=32\Rightarrow 20+(7-1)d=32(a=20,n=7)\Rightarrow 6d=32-20\Rightarrow 6d=12\Rightarrow d=2Now,A_1=a+d=20+2=22A_2=a+2d=20+2\times 2=24A_3=a+3d=20+3\times 2=26A_4=a+4d=20+4\times 2=28A_5=a+5d=20+5\times 2=30$

Thus, $22,24,26,28and30$ are five arithmetic means lying between 20 and 32.
Hence, a is the correct option.