Question

If the 8th term of an AP is 31 and it's 15th term is 16 more than the 13th term
find AP​

Answer 1

Answer:

8th term of AP = 31

⇒ a + (n-1)d = 31

a + (8-1)d = 31

a + 7d = 31

a = 31 - 7d — (i)

13th term of AP = y

⇒ a + (n-1)d = y

a + (13-1)d = y

a + 12d = y

15th term of AP = 16 + y

⇒ a + (n-1)d = 16 + y

a + (15-1)d = 16 + y

a + 14d = 16 + a + 12d  [y = a + 12d]

⇒ a + 14d = 16 + a + 12d

-12d + 14d = 16 + a - a

2d = 16

d = 8

Now, we find the value of ‘a’ by substituting the value of ‘d’ in equation (i):-

a = 31 - 7d

a = 31 - 7(8)

a = 31 - 56

a = -25

AP formed:-

-25, -17, -9, -1, 7, 15, 23, 31 ........

Hope it helps

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