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Question

The first term of an A.P. is 5 and its 100th term is 292. Find the 50th term of this A.P.

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Solution

Given first term of A.P is a1=5
100th term of A.P is a100=292

we know that the nth term of an A.P is given by
an=a1+(n1)d
hence 100th term can be written as
a100=a1+(1001)d
put value of a100=292 and a1=5 we get
292=5+99d
99d=2925
d=29799
d=3

now for finding 50th term put n=50,d=3 and a1=5 in eq(1) we get
a50=5+(501)(3)
a50=549×3
a50=5147
a50=142

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