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Question:

Find the 60th term of the AP 8, 10, 12, ..., if it has a total of 60 terms and hence find the sum of its last 10 terms.

Solution:

A.P is 8,10,12..
Then first term is 8 and common difference is 2.
an=a+(n−1)d.
Then
a60=8+(60−1)2=8+59×2=126
Last 10 term =a51,a52..a60
Then
a51=8+(51−1)2=108
So total of last 10 terms=10/2[108×2+(10−1)2]=5[216+18]=5[234]=1170