Multiple choice

Find the sum of the first $15$ terms of the following sequence having $n$th term as ${ y }_{ n }=9-5n\quad $

  1. $-390$
  2. $468$
  3. $-465$
  4. $-468$
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C Correct answer
Explanation

Sequence: y_n = 9 - 5n. This is an AP with a = 4, d = -5. Sum of 15 terms = (n/2)(2a + (n-1)d) = (15/2)(8 + 14*(-5)) = (15/2)(8 - 70) = (15/2)(-62) = 15 * -31 = -465.

AI explanation

The nth term of the sequence is given by the linear formula yn = 9 - 5n, meaning the sequence is an arithmetic progression with a first term of 4 and a common difference of -5. Using the arithmetic series sum formula Sn = n/2 * [2a + (n-1)d], we substitute n=15, a=4, and d=-5 to get S15 = 15/2 * [2(4) + (15-1)(-5)]. Solving the bracket gives 8 - 70 = -62, and multiplying by 15/2 yields a sum of -465.

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