Question

The sum of first six terms of an AP is 42 . The ratio of its 10th term to its 30th term is 1:3 Find the 20th term of AP

Answer 1

Since , the ratio of its 10th term to its 30th term is 1:3
(a+9d) / (a+29d) = 1 / 3
3a + 27d = a + 29d
2a = 2d
a = d (1)

Now, since Sum of first six terms of an AP is
42 = (6/2) * ( 2a + (6-1)d )
42 = 3 * ( 2a + 5d )
2a + 5d = 14
Now, By (1)
2a + 5a = 14
7a = 14
a = 2
Also , d = 2 [ By (1) ]

To calculate the 20th term of AP
a20 = a + 19d
a20 = 2 + 19*2
a20 = 40

So, the 20th term of AP is 40