Question 52
What is the sum of the following series?
-64, -66, -68,............., -100
Solution
The series is an A.P. with common difference, $$d = -66 - (-64) = -2$$
First term, $$a = -64$$ and last term $$a_n = -100$$
nth term of the series, $$a_n = a + (n - 1) d$$
=> $$-100 = -64 + (n - 1) (-2)$$
=> $$n - 1 = \frac{-36}{-2} = 18$$
=> $$n = 18 + 1 = 19$$
$$\therefore$$ Sum = $$\frac{n}{2} (a + a_n)$$
= $$\frac{19}{2} \times (-64 -100) = \frac{19}{2} \times (-164)$$
= $$19 \times (-82) = -1558$$
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