Question

IN aAP: the sum of 3rd and 5th terms of an a.p is 38 and sum of 7th and 10th terms of an a.p is 83,find the a.p

Answer 1

The AP is : 4 , 9 , 14 , 19...

According to the given data:

a + 2d + a + 4d = 38
⇒2a + 6d = 19 ...(i)

a + 6d + a + 9d = 83
⇒2a + 15d = 83 ...(ii)

Solving (i) and (ii):
9d = 45
⇒d = 5.
⇒a = 4

Hence forming the AP as (a) , (a + d) , (a + 2d) , ... , we get the above.

Answer 2

3rd term = a + 2d
5th term = a + 4d

A/Q,
a + 2d + a + 4d = 38
2a + 6d = 38-------(i)

7th term = a + 6d
10th tern = a + 9d
A/Q,
a + 6d + a + 9d = 83
2a + 15d = 83----------(ii)

Solving (i) and (ii)
9d = 45
d = 5

2a + 6 x 5= 38
2a = 8
a = 4

Required AP --->
4 , 9, 14,19,24.........