pritishmohan
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 preceding number . What is the value of \(a_1\)?
(1) \(a_2=15\)
(2) \(a_4 = 29\)
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 = a1So, 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 = 8Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: a4 = 29We already determined that a4 = 4k - 3
So, substitute 29 for a4 to get: 29 = 4k - 3
Solve:
k = 8Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent