Question :

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

Subject

Maths

Standard

Class 10

Views

485

Asked By

Chakrika

Aarohi
Answer / Solution

Solutions: We know, the nth term of the AP is;
an = a + (n − 1) d
a4 = a + (4 − 1) d
a4 = a + 3d

Thus, we can write,
a8 = a + 7d
a6 = a + 5d
a10 = a + 9d

Given in the question;

a4 + a8 = 24
a + 3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12 …………………………………………………… (i)
a6 + a10 = 44
a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22 …………………………………….. (ii)

On subtracting equation (i) from (ii), we get,
2d = 22 − 12
2d = 10
d = 5

From equation (i), we get,

a + 5d = 12
a + 5 (5) = 12
a + 25 = 12
a = −13
a2 = a + d = − 13 + 5 = −8
a3 = a2 + d = − 8 + 5 = −3

Therefore, the first three terms of this A.P. are −13, −8, and −3.

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