Question

If 10 times of 10th term is equal to 20 times of 20th term of an A.P. find its 30th term.

Answer 1

Let a be the first term and d be the common difference of the given A.P.

Given:
10a10 = 20a20
a10 = a + (10 - 1)d
[an = a + (n - 1)d]

a10 = a + 9d…………..(1)
a20 = a + (20 - 1)d
a20 = a + 19d………..(2)
10(a + 9d) = 20(a + 19d)

[From equation 1 and 2]

(a + 9d) = 20/10(a + 19d)
(a + 9d) = 2(a + 19d)
(a + 19d) = 2a + 38d
a - 2a = 38d -9d
-a = 29d
- a - 29d= 0
a +29d= 0………………..(3)
a30 = a + (30 -1)d
a30 = a + 29d
a30 = 0  [From equation 3 ]

a30 = 0 (zero]

Hence,the value of 30th term = 0 .

HOPE THIS WILL HELP YOU......

Answer 2

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