Question 82

The first and last terms of an arithmetic progression are 37 and -18. If the sum of the series is 114, then it has how many terms?

Solution

In an arithmetic progression with first term, $$a = 37$$ , last term, $$l = -18$$

Let number of terms = $$n$$

$$\therefore$$ Sum of A.P. = $$\frac{n}{2} (a + l) = 114$$

=> $$\frac{n}{2} (37 - 18) = 114$$

=> $$19n = 114 \times 2 = 228$$

=> $$n = \frac{228}{19} = 12$$

=> Ans - (B)

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The first and last terms of an arithmetic progression are 37 and ­-18. If the sum of the series is 114, then it has how many terms?