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Question

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


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


Mathematics
RD Sharma
Standard X

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