Question

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 13th term of the A.P.

Answer 1

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Answers-26

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Answer 2

SOLUTION

Let the term of the A.P. = a

& common difference= d

A/q

s6= 42

=) 6/2{ 2a+(6-1)d} =42

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

Further, it is given that

a10: a30= 1:3

$\frac{a + 9d}{a + 29d} = \frac{1}{3}$

=) 3a +27d= a+ 29d

=) 2a- 2d= 0

=) a-d= 0..............(2)

On solving (1)& (2) we get

=) a= d= 2

Therefore,

a13= a+ 12d

=) 2+12×2= 26

Hence, the first term= 2 & 13th term= 26

hope it helps ☺️⬆️