Question

Five arithmetic means are inserted between 6 and 36. Choose the correct numbers among the options.

• A. 12
• B. 16
• C. 26
• D. 28

Answer 1

Answer: (B), (C)

The correct options are
B

16

C

26

Let the required arithmetic means be $A_1$, $A_2$, $A_3$, $A_4$, and $A_5$.

$⟹$ 6, $A_1$, $A_2$, $A_3$, $A_4$, $A_5$ and 36 are in A.P.

$⟹$ 36=$7^{th}$ term of this A.P.

$⟹$ 36 = 6 + 6d i.e. d = 5

$⟹$ Required Arithmetic Means are $A_1$, $A_2$, $A_3$, $A_4$ and $A_5$

i.e. a + d, a + 2d, a + 3d, a + 4d, and a + 5d

= 6 + 5, 6 + 2$\times$5, 6 + 3$\times$5, 6 + 4$\times$5, and 6 + 2$\times$5

= 11, 16, 21, 26, and 31