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Find the sum of $- 37, - 33, - 29, . .$ upto $12$ terms.

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- 180

- 210

- 360

- 390

answer is A.

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Detailed Solution

The given series is

- 37, - 33, - 29, . . . . . . . . .

We have to find the sum of

- 37, - 33, - 29, . .

upto

12

terms.
Common difference,

d = a_{n + 1} - a_{n}

\Rightarrow

= - 33 - (- 37)

\Rightarrow d = - 33 + 37

\Rightarrow d

=4
The series is an AP with initial term a=37 and common difference, d = 4.
Number of terms, n =12
We know that,

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

\Rightarrow S_{12} = \frac{12}{2} [2 a + (12 - 1) d]

\Rightarrow S_{12} = \frac{12}{2} [2 \times - 37 + (12 - 1) \times 4]

\Rightarrow S_{12} = 6 [2 \times - 37 + 11 \times 4]

\Rightarrow S_{12} = 6 [- 74 + 44]

\Rightarrow S_{12} = 6 [30]

\Rightarrow S_{12} = - 180

Therefore, the sum of

- 37, - 33, - 29, . .

upto

12

terms is

- 180

.
Hence, option 1 is correct.

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