Question

If a, 7,b,23 are in AP find a and b. ​

Answer 1

Step-by-step explanation:

Since a, 7, b, 23 are in AP

∴ 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

Answer 2

7=a+b

23=a+3b

a+b+2b=7+2b

2b=16

b=8

a= -1

so,-1,7,15,23,31