Question

If 5 times the 5^th  term of an AP is equal to 15 times its 15^th  term, then the value of its 20^th  term will be _______

(a) 0

(b) 1

(c) 2

(d) 3

I got this question in an internship interview.

This question is from Nth Term of Arithmetic Progression in division Arithmetic Progressions of Mathematics – Class 10

Answer 1

The correct choice is (a) 0

For explanation I would say: 5(5^th term) = 15(15^th term)

5^th term = a + (5 – 1)d = a + 4d

15^th term = a + (15 – 1)d = a + 14d

5(a + 4d) = 15(a + 14d)

5a + 20d = 15a + 210d

20d – 210d = 15a – 5a

-190d = 10a

a = -19d

Now, the 20^th  term = a + (20 – 1)d = a + 19d

But a = -19d

Hence, -19d + 19d = 0