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Arithmetic Mean

If the nth te...

Question

If the $n^{t h}$ term of a sequence is given by $t_{n} = 7 n - 9$ , then the sum of first $100$ terms is

A

34455

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B

34450

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C

35450

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D

35550

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Solution

The correct option is B $34450$
As $t_{n} = 7 n - 9$ , which is a linear function of $n$ , so it is an A.P.
$a = t_{1} = - 2 d = t_{2} - t_{1} = 7$

Now, the sum of first $100$ terms
$S_{100} = \frac{100}{2} [2 \times (- 2) + 99 \times 7] ∴ S_{100} = 34450$

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Arithmetic Mean

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