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# Question 15. The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.

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This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6

In this question we have been given that the third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2.

Now we have to find the first term, the common difference and the sum of first 20 terms.

CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 15

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1. Given A.P. has third term(a3) = 7 and seventh term(a7) = 3a3Â + 2 = 3(7) + 2 = 23.

We know nth term of an A.P. is given by, anÂ = a + (n âˆ’ 1)d. So, we get,

a + 2d = 7 â€¦.. (1)

a + 6d = 23 â€¦.. (2)

Subtracting (1) from (2), we get,

=> (a + 6d) âˆ’ (a + 2d) = 23 âˆ’ 7

=> 4d = 16

=> d = 4

On putting d = 4 in (1), we get,

=> a + 2(4) = 7

=> a = 7 âˆ’ 8

=> a = âˆ’1

We know sum of n terms of an A.P. is given by SnÂ = n[2a + (n âˆ’ 1)d] / 2.

Here a = âˆ’1, d = âˆ’4, n = 20. So sum is,

S20Â = 20[2(âˆ’1) + (20 âˆ’ 1)(4)]/2

= 20[-2 + 76]/2

= 20[39] = 740

Hence, the sum of first 20 terms for the given A.P. is 740.

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