Question

If the term of an AP is 31 and the 15th term is 16 more than the 11th term, find the AP.

Answer 1

Hey friend !

Here's your answer
___________________________________________

a8 = 31

a + (n-1) d = 31

a + (8-1) d = 31

a + 7d =31 .............................(i)


a15 = a11 + 16

a + (n-1) d = a + (n-1) d + 16

a + (15-1) d = a + (11-1) d + 16

a + 14d - a - 10d = 16

4d = 16

d = 16/4 = 4

• Putting the value of D by equation (i) ;

a + 7d = 31

a + 7 × 4 = 31

a + 28 = 31

a = 31 - 28

a = 3

[ d = 4 and a = 3 ]
______________________________

♡ Hope this helps !

Answer 2

a8 = 31

a + (n-1) d = 31

a + (8-1) d = 31

a + 7d =31 .............................(i)

a15 = a11 + 16

a + (n-1) d = a + (n-1) d + 16

a + (15-1) d = a + (11-1) d + 16

a + 14d - a - 10d = 16

4d = 16

d = 16/4 = 4

• Putting the value of D by equation (i) ;

a + 7d = 31

a + 7 × 4 = 31

a + 28 = 31

a = 31 - 28

a = 3

[ d = 4 and a = 3 ]