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Question

In an arithmetic progression the third term is four times the first term, and the sixth term is 17, then 20th term of the progression is

A
57
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B
59
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C
61
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D
None of these
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Solution

The correct option is B 59
Let a,d be the first term and the common difference of the A.P.
Then the third term is a+(31)d=a+2d.
According to the problem,
a+2d=4a
or 3a=2d
or, a=2d3......(1).
Also given the sixth term is 17.
Then,
a+5d=17
or, 17d3=17 [Using (1)]
or, d=3a=2.......(2).
Now the 20 th term of the A.P. is
=a+19d
=2+57=59 [ Using (2)]

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