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The sequence 3, -6, 9, -12,... is formed by taking all positive multip
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05 Mar 2022, 04:00
05 Mar 2022, 04:00
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70% (02:06) correct
30% (01:59) wrong based on 10 sessions
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The sequence 3, -6, 9, -12,... is formed by taking the positive multiples of 3 in increasing order and changing each even term to its negative. What is the sum of the first 100 terms?
Show: ::
-150
Re: The sequence 3, -6, 9, -12,... is formed by taking all positive multip
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07 Mar 2022, 11:15
07 Mar 2022, 11:15
Thanks for the question Carcass, will wait for the OE
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Re: The sequence 3, -6, 9, -12,... is formed by taking all positive multip
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07 Mar 2022, 11:26
07 Mar 2022, 11:26
3
Carcass wrote:
The sequence 3, -6, 9, -12,... is formed by taking all positive multiples of 3 in increasing order and changing each even term to its negative. Then what is the sum of the first 100 terms?
Show: ::
-150
Sum of the first 100 terms = 3 + (-6) + 9 + (-12) + 15 + (-18) + . . . . . + 297 + (-300)
Rewrite to get: Sum of the first 100 terms = [3 + (-6)] + [9 + (-12)] + [15 + (-18)] + . . . . . + [297 + (-300)]
Notice that the sum of each pair of values is always -3
So, the sum of the first 100 terms = [-3] + [-3] + [-3] + . . . . . + [-3]
At this point, all we need to do is determine how many -3's we must add together
Since there are 100 terms all together, we know that there are 50 PAIRS of values, and each pair sums to -3
So, the sum of the first 100 terms = 50(-3) = -150
Answer: -150
