Question

find the 12th term from the last of the A.P. 1,4,7,10,.....,88

Answer 1

88=1+(n-1)3

87=(n-1)3

n-1=29

n=30

hence there are 30 terms in ap

12th term from last=18th term from first

18th term=1+17×3

=1+51=52

hence 12th term from last is 52

Answer 2

This series of numbers is in an a.p. with first term 1 and the common difference 3. So according to the formula a+(n-1)*d, where a is the first term of the series and n is the total number of terms in the series and d is the common difference. The total number of terms in the series is n=30. Now, we are asked to find the 12th term from the last of this a.p. So it is equivalent to find the (30-12)+1 th term of this a.p. Hence, the required term,according to the previous formula, is 1+(19-1)*3=55.