Question

The sum of 4th and 8th terms of an AP is 16th and the sum of the 6th term and the 10th term is 30.Find the AP.

Answer 1

Heya !!!

This is your answer......

Given :-
4th and 8th terms of an AP is 16.
So.
a4 + a8 = 16.

a + 3d + a + 15d = 16
2a + 18d = 16.
= a + 9d = 8. .......(i).

Also....
sum of the 6th term and the 10th term is 30.
so....
a6 + a10 = 30.
a+5d + a + 9d = 30.
2a + 14d = 30.
a + 7b = 15. .. .......(ii).

Subtracting equation (ii) from (i).

we get .....

a + 9d = 8
a + 7d = 15
- - -
----------------
2d = -7
d = -7/2.
Putting d = -7/2 in equation (i).


a - 49/2 = 15
a = 30/2 + 49/2
a = 79/2.

Now.....
a = 79/2.
a + d = 77/2.
a + 2d = 75/2.
a+ 3d = 73/2.

Hence the AP is 79/2, 77/2, 75/2, 73/2, .......