Question

The value of a,b and c such that the numbers a, 7, b, 23 and c are in AP are

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

c) a=-1,b=-15,c=-31 d) a=1,b= -15,c=31​

Answer 1

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