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Question

Determine the nth term of the AP whose 7th term is −1 and 16th term is 17.

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Solution

Let a be the first term and d be the common difference of the AP. Then,
a7=1

a+(71)d=1 [nth term is given by an=a+(n1)d]

a+6d=1(i)

Also, a16=17

a+15d=17(ii)

From eq. (i) and (ii), we get
16d+15d=17 [a=16d from eq.(i)]

9d=17+1

d=2
Putting d=2 in eq.(i), we get
a+6×2=1

a=112=13
an=a+(n1)d=13+(n1)×2

=13+2n2=2n15
Hence, the nth term of the AP is (2n15).


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