Q. 10 A4.2( 10 Votes )

Find the 10th term form the end of the AP 4, 9, 14, .. , 254.

Answer :

The above series of numbers forms an arithmetic progression with


first term(a) = 4 and,


common difference(d) = (n + 1)th term – nth term = 9 – 4 = 5


last term or nth term(an) = 254


Let the total no. of terms in above A.P be n.


an = a + (n – 1) × d


254 = 4 + (n – 1) × 5


250 = 5n – 5


5n = 255


n = 51


10th term from the end of AP = 51 – 10 + 1 = 42th term from the beginning


42th term = a42 = a + (42 – 1)d


= 4 + 41 × 5


= 209


Hence, 10th term from the end of AP is 209.


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