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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. - Mathematics

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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.

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Solution

We know that,

an = a + (n − 1) d

a4 = a + (4 − 1) d

a4 = a + 3d

Similarly,

a8 = a + 7d

a6 = a + 5d

a10 = a + 9d

Given that, a4 + a8 = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12 (1)

a6 + a10 = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 (2)

On subtracting equation (1) from (2), we obtain

2d = 22 − 12

2d = 10

d = 5

From equation (1), we obtain

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.

Concept: nth Term of an AP
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APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.2 | Q 18 | Page 107
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