S is a sequence s1, s2, s3,…,sn in which every term after the first is

Question

S is a sequence s1, s2, s3, …, sn in which every term after the first is one less than three times the previous term. If s5 – s3 = 28, which of the following is the first term in the sequence?

A. 2/3 
B. 8/9 
C. 1 
D. 5/3 
E. 2

PKN · Accepted Answer

s5-s3=28
or, 3s4-1-s3=28
or, 3(3s3-1)-1-s3=28
or, 8s3=32
or, s3=4
or, 3s2-1=4
or, 3(3s1-1)=5
or, 9s1=8
or, s1=8/9

Ans. (B)

ScottTargetTestPrep · Answer

Solution:

S1 = n

S2 = 3n - 1

S3 = 9n - 3 - 1 = 9n - 4

S4 = 27n - 12 - 1 = 27n - 13

S5 = 81n - 39 - 1 = 81n - 40

Since S5 - S3 = 28:

81n - 40 - (9n - 4) = 28

81n - 40 - 9n + 4 = 28

72n = 64

n = 64/72 = 8/9

Alternate Solution:

Instead of letting S1 = n, we can let S3 = n, so we have:

S4 = 3n - 1

S5 = 9n - 3 - 1 = 9n - 4

Since S5 - S3 = 28:

9n - 4 - n = 28

8n = 32

n = 4

Now, letting s = S2 (the second term), we have:

3s - 1 = 4

3s = 5

s = 5/3

Finally, letting f = S1 (the first term), we have:

3f - 1 = 5/3

3f = 8/3

f = 8/9

Answer: B

Kaichi · Answer

S is a sequence s1, s2, s3, ..., sn in which every term after the first is one less than three times the previous term. If s5 – s3 = 28, which of the following is the first term in the sequence?

When I was doing this via the forum quiz, I initially wanted to make an equation for this, but upon understanding the question I already took up 20~30s out of my 120 seconds.

I noticed the answers available, with 1 as the middle term. If we can determine how big of a gap s5 - s3 is by plugging S1 = 1, we can narrow the answer down to A/B or D/E (If gap is >28, means S1 needs to be <1)

If S1 = 1,
S2 = 3 - 1 = 2
S3 = 6 - 1 = 5
S4 = 15 - 1 = 14
S5 = 42 - 1 = 41

41 - 5 is 36, therefore, we know S1 has to be <1. Which narrows the answer to A/B

If S1 = 8/9 (B),
S1 = 8/9
S2 = 8/3 - 1 = 5/3
S3 = 5 - 1 = 4
S4 = 12 - 1 = 11
S5 = 33 - 1 = 32

32-4 = 28.

We could also plug in A's value and eliminate A.
This effectively took me less than 120 seconds.
Cheers.

bumpbot · Answer

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S is a sequence s1, s2, s3,…,sn in which every term after the first is

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