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CBSE Class 10 Answered

The sum of first six terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1:3. Find the first and the thirteenth term of the A.P.
Asked by Topperlearning User | 22 Sep, 2017, 09:32: AM
Expert Answer

Let 'a' be the first term and 'd' be the common difference.

S6 = 42

2a + 5d = 14

2a = 14 - 5d ...(1)

begin mathsize 12px style fraction numerator 14 minus 5 straight d plus 18 straight d over denominator 14 minus 5 straight d plus 58 straight d end fraction equals 1 third space space space space space from space left parenthesis 1 right parenthesis fraction numerator 14 plus 13 straight d over denominator 14 plus 53 straight d end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction end style

42 + 39d = 14 + 53d

28 = 14d

d = 2

From (1),

2a + 5d = 14a = 2

Now, a13 = 2 + 12 2 = 26

Answered by | 22 Sep, 2017, 11:32: AM

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