Question

if 8th term of an ap is 31 and 15 term of an ap is 16 more than 11 term
find AP​

Answer 1

Answer:

59, 55, 51, 47,...

Step-by-step explanation:

a8 = a+7d = 31     -i

a15 = 16+a11

a+14d = 16+a+10d

-4d = 16

d = -4

then, fom equation i

a = 59

then AP,

59, 55, 51, 47

Answer 2

Answer:

8th term of AP = 31

⇒ a + (8-1)d = 31

a + 7d = 31

a = 31 - 7d — (i)

Let 11th term of AP = y

⇒ a + (11-1)d = y

a + 10d = y

15th term of AP = 16 + y

⇒ a + (15-1)d = 16 + y

a + 14d = 16 + a + 10d [y = a + 10d]  

⇒ a + 14d = 16 + a + 10d

14d - 10d = 16 + a - a

4d = 16

d = 4

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

⇒ a = 31 - 7d

a = 31 - 7(4)

a = 31 - 28

a = 3

AP formed:-

3, 7, 11, 15, 19, 23, 27, 31 .........

Hope it helps

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