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Question

Which terms of the A.P.3,15,27,39,... will be 120 more than its 21st term ?

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Solution

The given A.P.3,15,27,39,

Here First term a =3

Common difference d= 12

Hence T21 = a +(21-1)d

=a+20d

=3+240

=243

Also given

Tn = 120 + 243 Further we know that Tn = a+ (n-1) d
= 363 = 3 + (n-1) d
Equating 363= Tn = 3 + (n-1) d
363=3+(n-1)12

or 363= 3 +12n -12

or 363 = 12n -9

or 363+9 =12n

or 372 =12n

37212 =n


n=31
Hence the 31st term = 363


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