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GMAT Practice Question (One of Hundreds)
n1 = 145, n2 = 147, n3 = 149
The above is an arithmetic sequence. The nth term in this sequence is equal to n2. What is n?
Correct Answer: E
The equation for an arithmetic sequence is an = a1 + d(n-1)
- The equation for an arithmetic sequence is an = a1 + d(n-1) where d stands for the how much the sequence goes up each term while a1 stands for the first term in the sequence. Thus the equation of the above sequence is an = 145 + 2(n-1).
- Setting an to n2 gives us n2 = 145 + 2(n-1). This is a quadratic equation. Algebraic manipulation results in:
n2 = 145 + 2(n-1)
n2 = 145 + 2n - 2
n2 - 2n - 143 = 0
- Factoring leads us to the equation
(n + 11)(n - 13) = 0
- Thus our two solution are n = -11 and n = 13. There is no such thing as the -11 term in the sequence so n must be 13.
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