Question

The sum of first six terms of an arithmetic progression is 42 . the ratio of its 10 and 30 term is 1:3 . calculate the first term and 13 term of the progression

Answer 1

Step-by-step explanation:

S6 = 42

S6 = 6/2{2a+(6-1)d}

42 = 3(2a + 5d)

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

a10/a30 = 1/3

a + 9d/a +29d = 1/3

3(a + 9d) = a + 29d

3a + 27d = a + 29d

3a - a = 29d - 27d

2a = 2d

a = d

put the value of (a) in eqn(1)

14 = 2a + 5d

14 = 2d + 5d

14 = 7d

2 = d

a = 2 ( first term)

a13 = a + 12d

= 2 + 12×2

= 2 + 24 = 26 (Ans)