Going from the 1st term (30) to the 17th term (-18), you have a change of -48 and make 16 "steps" between.
-48 / 16 = -3
So the common difference (d) is -3
As for the sum, we can just use the formula. The sum is the average of the first and last term times the number of terms:
S[17] = (u1 + u17)/2 * 17
S[17] = (30 + -18)/2 * 17
S[17] = 12/2 * 17
S[17] = 6 * 17
S[17] = 102
If you wanted to double-check, write down all the terms and add them up:
30 + 27 + 24 + 21 + 18 + 15 + 12 + 9 + 6 + 3 + 0 + -3 + -6 + -9 + -12 + -15 + -18
Note: we can cancel 18 with -18, etc. so the last terms all give a total of 0.
= 30 + 27 + 24 + 21
= 102
Copyright © 2024 1QUIZZ.COM - All rights reserved.
Answers & Comments
Going from the 1st term (30) to the 17th term (-18), you have a change of -48 and make 16 "steps" between.
-48 / 16 = -3
So the common difference (d) is -3
As for the sum, we can just use the formula. The sum is the average of the first and last term times the number of terms:
S[17] = (u1 + u17)/2 * 17
S[17] = (30 + -18)/2 * 17
S[17] = 12/2 * 17
S[17] = 6 * 17
S[17] = 102
If you wanted to double-check, write down all the terms and add them up:
30 + 27 + 24 + 21 + 18 + 15 + 12 + 9 + 6 + 3 + 0 + -3 + -6 + -9 + -12 + -15 + -18
Note: we can cancel 18 with -18, etc. so the last terms all give a total of 0.
= 30 + 27 + 24 + 21
= 102