Question

the sum of the 4th and 8th term of an ap is 24 and the sum of 6th and 10th term is 44 find the first five terms of an ap​

Answer 1

EXPLANATION.

• GIVEN

TO FIND FIRST FIVE TERM OF AN AP.

we know that,

An = a + ( n - 1 ) d

sum of the 4th and 8th term of an Ap = 24

A4 = a + 3d

A8 = a + 7d

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12 ......(1)

sum of 6th and 10th term is 44

A6 = a + 5d

A10 = a + 9d

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 ....(2)

From equation (1) and (2)

we get,

-2d = - 10

d = 5

put d = 5 in equation (1)

we get,

a + 5(5) = 12

a + 25 = 12

a = -13

First five term of an ap.

First term = a = -13

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

Third term = a + 2d = - 13 + 2(5) = -3

Fourth term = a + 3d = -13 + 3(5) = 2

Fifth term = a + 4d = -13 + 4(5) = 7

Therefore,

First five term of an ap =

-13,-8,-3,2,7 ....