Which term of the A.P. will be 120 more than its 21st term?

a = 3, d = 15 – 3 = 12

Let last term be an


an = a + (n – 1) d


= 3 + (n – 1) 12


= 12n – 9 (i)


a21 = a + 20d


= 3 + 20(12) = 243


Now, the term is 120 more than the 21st term


an = 120 + a21


= 120 + 243


= 363


Putting this value in (i), we get


363 = 12n – 9


12n = 363 + 9


n = 31


Hence, 31st term of given A.P. is 120 more than its 21st term


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