# CBSE Class 10 Answered

**The sum of first six terms of an arithmetic progression is 42. The ratio of its 10**

^{th}term to its 30^{th}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.

S_{6} = 42

_{}

2a + 5d = 14

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

_{}

_{}

_{}

42 + 39d = 14 + 53d

28 = 14d

_{}d = 2

From (1),

2a + 5d = 14_{}a = 2

Now, a_{13} = 2 + 12 _{}2 = 26

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

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