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Question

Is 150 a term of the A.P. 11,8,5,2,.....?

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Solution

Ans.
given A.P is
11,8,5,2,.....
first term of this A.P is a1=11
second term of this A.P is a2=8
common difference of an A.P is given by
(i.e.,d=an+1an)
putting n=1 in above equation
d=a2a1=811=3
hence common difference for this A.P is d=3
the nth term of an A.P is given by.
an=a1+(n1)d
an=11+(n1)(3)
an=113n+3
an=143n...eq(1)
we have to find is an=150 is a term of this A.P
put an=150 in eq(1)
150=143×n
3×n=150+14
n=1363
n=45.33
but we know that n can't be an fractional number, it must be an integer(i.e., we can't have 45.33th term in our A.P)
hence 150 is not an term of this A.P

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