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Question

Which term of the A.P. 4,9,14,..... is 254?

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Solution

Given A.P is 4,9,14,,.....
first term of this A.P is a1=4
second term of this A.P is a2=9
common difference of an A.P is given by
(i.e.,d=an+1an)
putting n=1 in above equation
d=a2a1=94=5
hence common difference for this A.P is d=5
the nth term of an A.P is given by.
an=a1+(n1)d
an=4+(n1)(5)
an=4+5n5
an=1+5n...eq(1)
we have to find which term(n) of this A.P is an=254
put an=254 in eq(1)
254=1+5×n
5×n=254+1
5×n=255
n=2555
n=51
hence 51th term of this A.P is 254

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