Question

If following numbers are in AP : a, 7, b, 23, c, then evaluate : a – 2b + c.

Answer 1

Answer:

a - 2b + c = 0

Step-by-step explanation:

The AP has the terms a , 7 , b , 23 , c

$\frac{a+b}{2}$ = 7

⇒a+b = 14 -----> (1)

Similarly,

$\frac{b+c}{2}$ = 23

⇒ b+c = 46 -----> (2)

(2) - (1)

⇒ c - a = 32

⇒ a = c - 32 -----> (3)

From (1)

b = 14 - a

⇒ b = 14 - (c - 32)

⇒ b = 46 - c -----> (4)

On sub. (3) & (4) in the AP we get

c - 32 , 7 , 46 - c , 23 , c

$\frac{7+23}{2}$ = 46 - c

⇒ 15 = 46 - c

⇒ c = 31

On sub. in (3) & (4)

a = 31 - 32 = -1

b = 46 - 31 = 15

⇒ a - 2b + c = -1 - 2(15) + 31 = -1 - 30 + 31 = 31 - 31 = 0  

∴ a - 2b + c = 0