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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Last term=118, Sum=1320

Last term=126, Sum=1170

Last term=135, Sum=1189

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 [2 a + (n − 1) d]

Then equation (1) becomes,

= 602 [2 × 8 + (60 − 1) × 2] − 502 [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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