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.

Maths

Class 10

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485

Chakrika

Aarohi

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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