Question

The sum of 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44
Find the first three sums of AP.

Answer 1

Given

The sum of 4th and 8th term=24

The sum of 6th and 10th term=44

Let:

The first term of AP=a

The common difference=d

A.T.Q:

•Using formula here

=>Tn=a+(n-1)d

=>Sum of 4th and 8th term=24

=>a+3d+a+7d=24

=>2a+10d=24

Dividing by 2 on both sides

=>a+5d=12-------(1)

=>Sum of 6th and 10th term=44

=>a+5d+a+9d=44

=>2a+14d=44

Dividing by 2 on both sides here

=>a+7d=22------(2)

Now , solving eq 1 and 2 by subtracting

=>a+5d=12

=>a+7d=22

By solving we get,

=>-2d=-10

=>d=5

Putting the value of d=5 in EQ 1

=>a+5d=12

=>a+25=12

=>a=12-25

=>a=-13

hence,

Three terms of AP are

-13+5=-8

-8+5=-3

AP are -13, -8 ,-3

Answer 2

GIVEN:

Sum of 4th and 8th term of AP = 24

Sum of 6th and 10 terms fo AP = 44

TO FIND:

First three terms of AP

SOLUTION:

4th term: a + 3d and 8th term: a + 7d

==> a + 3d + a + 7d = 24

=> 2a + 10d = 24 ---(1)

6th term: a + 5d and 10th term = a + 9d

==> a + 5d + a + 9d = 44

==> 2a + 14d = 44 ----(2)

After solving both equation,

==> -4d = -20

==> d = 20/4

==> d = 5

Common Difference = 5

Substitute (d) in eq - (1)

==> 2a + 10d = 24

==> 2a + 10(5) = 24

==> 2a + 50 = 24

==> 2a = 24 - 50

==> a = -26/2

==> a = -13

First term = -13

The first terms are:

First term = a = -13

Second term = a + d = -13 + 5 = -8

Third term = a + 2d = -13 + 10 = -3

Therefore, the first three terms are -13, -8 and -3.