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Question

For an A.P., the seventh term is 19 and the thirteenth term is 37. Find its twenty second term.

A
60
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B
54
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C
64
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D
78
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Solution

The correct option is C 64
For the given A.P., T7=19 and T13=37
Now Tn=a+(n1)d
T7=a+(71)d
19=a+6d
a+6d=19 ............ (1)
Again, T13=a+(131)d
37=a+12d
a+12d=37 ............. (2)
Subtracting eq. (1) from eq. (2)
a+12d=37
a+6d=19
6d=18
d=13
Substituting d=13 in a+6d=19,
a+6(3)=19
a+18=19
a=1
Thus, the first term of the A.P. is 1 and the common difference is 3.
Now, T22=a+(221)d=1+(221)(3)
=1+(21)(3)=1+63=64
Thus, the twenty second term of the given A.P. is 64.

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