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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. - CBSE Class 10 - Mathematics

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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.

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.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 5: Arithmetic Progressions
Ex. 5.20 | Q: 18 | Page no. 107
Solution 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. Concept: nth Term of an AP.
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