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Q.

An AP 8,10,12, ..... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms from the choices given below.


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a

Last term=118, Sum=1320

b

Last term=126, Sum=1170

c

Last term=135, Sum=1189 

d

Last term=101, Sum=1078

answer is C.

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Detailed Solution

The given AP is 8,10,12, ..... and has 60 terms.
We have to find the last term and the sum of the last 10 terms.
Here,
a=8,
d=10-8=2,
n=60
Since, the last term is given by,
a n =a+ n−1 d
a 60 =8+(60−1)2 =8+59(2) =126
The last term is 126.
The sum of the last 10 terms is given as,
S 10 = S 60 − S 50      …(1)
We know that sum of n-terms in AP is,
S n = n 2 [2a+(n−1)d]
Then equation (1) becomes,
= 60 2 [2×8+(60−1)×2]− 50 2 [2×8+(50−1)×2] =30×(16+118)−25×(16+98) =30×134−25×114
On solving the above values,
=4020−2850 =1170
The sum of the last 10 terms is 1170.
Hence, option 3) is correct.
 
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An AP 8,10,12, ..... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms from the choices given below.