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## $$S$$ is a sequence $$s_1, s_2, s_3, \ldots, s_n$$ in which every term after the first is one less than three times the

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### $$S$$ is a sequence $$s_1, s_2, s_3, \ldots, s_n$$ in which every term after the first is one less than three times the

by Gmat_mission » Wed Jun 24, 2020 8:08 am

00:00

A

B

C

D

E

## Global Stats

$$S$$ is a sequence $$s_1, s_2, s_3, \ldots, s_n$$ in which every term after the first is one less than three times the previous term. If $$s_5 - s_3 = 28,$$ which of the following is the first term in the sequence?

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

[spoiler]OA=B[/spoiler]

Source: Princeton Review

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### Re: $$S$$ is a sequence $$s_1, s_2, s_3, \ldots, s_n$$ in which every term after the first is one less than three times

by deloitte247 » Fri Jun 26, 2020 12:14 am
$$Let\ s_1=x$$
$$s_2=3x-1$$
$$s_3=3\left(3x-1\right)-1=9x-3-1=9x-4$$
$$s_4=3\left(9x-4\right)-1=27x-12-1=27x-13$$
$$s_5=3\left(27x-13\right)-1=81x-39-1=81x-40$$
$$Given\ that\ \ s_5-s_3=28$$
$$\left(81x-40\right)-\left(9x-4\right)=28$$
$$81x-40-9x+4=28$$
$$81x-9x=28+36$$
$$\frac{72x}{72}=\frac{64}{72}$$
$$x=\frac{64}{72}=\frac{16}{18}=\frac{8}{9}$$
$$Answer\ =\ B$$

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### Re: $$S$$ is a sequence $$s_1, s_2, s_3, \ldots, s_n$$ in which every term after the first is one less than three times

by Scott@TargetTestPrep » Mon Jun 29, 2020 5:54 am
Gmat_mission wrote:
Wed Jun 24, 2020 8:08 am
$$S$$ is a sequence $$s_1, s_2, s_3, \ldots, s_n$$ in which every term after the first is one less than three times the previous term. If $$s_5 - s_3 = 28,$$ which of the following is the first term in the sequence?

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

[spoiler]OA=B[/spoiler]

Solution:

Let can let s1 = x, so in terms of x, we see that

s2 = 3x - 1,

s3 = 3(3x - 1) - 1 = 9x - 4,

s4 = 3(9x - 4) - 1 = 27x - 13, and

s5 = 3(27x - 13) - 1 = 81x - 40.

Since s5 - s3 = 28, in terms of x, we have:

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

72x - 36 = 28

72x = 64

x = 64/72 = 8/9