Question

find a and b if a, 7 ,b, 23 are in AP​

Answer 1

Answer:

Since a, 7, b, 23 and c are in AR

∴ 7 - a = b - 7 = 23 - b = c - 23 = common difference

I II III IV

Taking second and third terms, we get

b - 7 = 23 - b

⇒ 2b = 30

∴ b = 15

Taking first and second terms, we get

7 - a = b - 7

⇒ 7 - a = 15 - 7

⇒ 7 - a = 8

∴ a = -1

Taking third and fourth terms, we get

23 - b = c - 23

⇒ 23 - 15 = c - 23

⇒ 8 = c - 23

⇒ 8 + 23 = c ⇒ c = 31

Hence, a = -1, b = 15, c = 31

Answer 2

Answer:

a=9 , b=16 as b+7= 23 and a+7=16