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Sequence S is such that S_n=S_n-1+3/2
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03 Jun 2020, 05:55
03 Jun 2020, 05:55
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67% (02:26) correct
32% (02:14) wrong based on 88 sessions
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Sequence \(S\) is such that \(S_n=S_{n-1}+\frac{3}{2}\) and \(S_1=2\)
Sequence \(A\) is such that \(A_n=A_{n-1}-1.5\) and \(A_1=18.5\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Sequence \(A\) is such that \(A_n=A_{n-1}-1.5\) and \(A_1=18.5\)
Quantity A |
Quantity B |
The sum of the terms in S from \(S_1\) to \(S_{13}\), inclusive |
The sum of the terms in A from \(A_1\) to \(A_{13}\), inclusive |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: Sequence S is such that S_n=S_n-1+3/2
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03 Jun 2020, 05:56
03 Jun 2020, 05:56
Expert Reply
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Re: Sequence S is such that S_n=S_n-1+3/2
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03 Jun 2020, 06:10
03 Jun 2020, 06:10
1
Carcass wrote:
Sequence \(S\) is such that \(S_n=S_{n-1}+\frac{3}{2}\) and \(S_1=2\)
Sequence \(A\) is such that \(A_n=A_{n-1}-1.5\) and \(A_1=18.5\)
Sequence \(A\) is such that \(A_n=A_{n-1}-1.5\) and \(A_1=18.5\)
Quantity A |
Quantity B |
The sum of the terms in S from \(S_1\) to \(S_{13}\), inclusive |
The sum of the terms in A from \(A_1\) to \(A_{13}\), inclusive |
Let's list some terms for each set..
Sequence S
S1 = 2
S2 = 2 + 1.5 (add one 1.5)
S3 = 2 + 1.5 + 1.5 (add two 1.5's)
S4 = 2 + 1.5 + 1.5 + 1.5 (add three 1.5's)
.
.
.
S13 = 2 + 1.5 + 1.5 + 1.5 + 1.5 + 1.5 + 1.5 ..... (add twelve 1.5's)
So, S13 = 2 + (12)(1.5) = 20
Sequence S = 2, 3.5, 5, 6.5,...., 18.5, 20
-------------------
Sequence A
A1 = 18.5
A2 = 18.5 - 1.5 (subtract one 1.5)
A3 = 18.5 - 1.5 - 1.5 (subtract two 1.5's)
A4 = 18.5 - 1.5 - 1.5 - 1.5 (subtract three 1.5's)
.
.
.
A13 = 18.5 - 1.5 - 1.5 - 1.5 (subtract twelve 1.5's)
So, A13 = 18.5 - (12)(1.5) = 0.5
Sequence A = 18.5, 17, 15.5,....2, 0.5
--------------------
We get:
Quantity A: 2 + 3.5 + 5 + 6.5 +....+ 18.5 + 20
Quantity B: 18.5 + 17 + 15.5 +....+ 2 + 0.5
At this point, we can probably see that both sums have many values in common, and when we examine the remaining numbers, we can see that quantity A is greater.
If you're not convinced, we can also subtract 2, 3.5, 5,...,17 and 18.5 from both quantities to get:
Quantity A: 20
Quantity B: 0.5
Answer: A
Cheers,
Brent
