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) \(a_4=29\)

Answer: D

Source: GMAT Prep

## 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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## Global Stats

**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

Answer: D

Cheers,

Brent