Multiple choice

Find the sum of the first $15$ terms of the following sequences having $n$th term as ${ x }_{ n }=6-n$

  1. $30$
  2. $-30$
  3. $20$
  4. $-20$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

x_n = 6 - n. Sum = sum_{n=1}^{15} (6 - n) = 6*15 - (15*16)/2 = 90 - 120 = -30.

AI explanation

Substitute n = 15 into the given nth term formula to find the 15th term, which gives x_15 = 6 - 15 = -9. The first term x_1 is 6 - 1 = 5. Since the sequence decreases by 1 each time, it forms an arithmetic progression. Using the arithmetic progression sum formula, S_n = n/2 * (first term + last term), the sum is 15/2 * (5 + (-9)), which equals 15/2 * (-4) = -30.

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