An AP 5,12,19, .... has a total of 50 terms. Find its last term. Hence, find the sum of its last 15 terms from the choices given below.

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338, 4466

348, 4485

342, 4477

350, 4488

answer is B.

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Detailed Solution

The given AP is 5, 12, 19, .... and has 50 terms.
We have to find the last term and the sum of last 15 terms.
Here,
a=5,
d=12-5=7,
n=50
We know that, the nth term of an AP is given by,

a n = a + (n − 1) d

On putting the given values in the above formula,
The last term is given by,

a 50 = 5 + (50 − 1) 7 = 5 + 49 (7) = 348

The last term is 348.
And the sum of the last 15 terms is given by,

S 15 = S 50 − S 35

…(1)
We know that sum of n-terms in AP is,

S n = n 2 [2 a + (n − 1) d]

Then equation (1) becomes,

= 502 [2 × 5 + (50 − 1) × 7] − 352 [2 × 5 + (35 − 1) × 7] = 502 × (10 + 343) − 352 × (10 + 238) = 502 × 353 − 352 × 248

On solving the above values,

= 17650 − 8680 2 = 89702 = 4485

The sum of the last 15 terms is 4485.
Hence, option 2) is correct.

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