## The sequence of four numbers $$a_1, a_2, a_3$$ and $$a_4$$ is such that each number after the first is $$a_1-1$$ greater

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### The sequence of four numbers $$a_1, a_2, a_3$$ and $$a_4$$ is such that each number after the first is $$a_1-1$$ greater

by Vincen » Sat Dec 04, 2021 7:38 am

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The sequence of four numbers $$a_1, a_2, a_3$$ and $$a_4$$ is such that each number after the first is $$a_1-1$$ greater than the preceding number. What is the value of $$a_1?$$

(1) $$a_2=15$$

(2) $$a_4=29$$

Source: GMAT Prep

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### Re: The sequence of four numbers $$a_1, a_2, a_3$$ and $$a_4$$ is such that each number after the first is $$a_1-1$$ gre

by [email protected] » Sun Dec 05, 2021 6:42 am

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## Global Stats

Vincen wrote:
Sat Dec 04, 2021 7:38 am
The sequence of four numbers $$a_1, a_2, a_3$$ and $$a_4$$ is such that each number after the first is $$a_1-1$$ greater than the preceding number. What is the value of $$a_1?$$

(1) $$a_2=15$$

(2) $$a_4=29$$

Source: GMAT Prep
Given: The sequence of four numbers a1, a2, a3 and a4 is such that each number after the first is a1 - 1 greater than preceding number
Let k = a1
So, each term after a1 is k - 1 greater than the term before it.

So we have:
a1 = k
a2 = k + (k - 1) = 2k - 1
a3 = 2k - 1 + (k - 1) = 3k - 2
a4 = 3k - 2 + (k - 1) = 4k - 3

Target question: What is the value of k?

Statement 1: a2 = 15
We already determined that a2 = 2k - 1
So, substitute 15 for a2 to get: 15 = 2k - 1
Solve: k = 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a4 = 29
We already determined that a4 = 4k - 3
So, substitute 29 for a4 to get: 29 = 4k - 3
Solve: k = 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT