# Practice GMAT Questions

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_{1}= 145, n

_{2}= 147, n

_{3}= 149

The above is an arithmetic sequence. The n

^{th}term in this sequence is equal to n

^{2}. What is n?

**E**

_{n}= a

_{1}+ d(n-1)

- The equation for an arithmetic sequence is a
_{n}= a_{1}+ d(n-1) where d stands for the how much the sequence goes up each term while a_{1}stands for the first term in the sequence. Thus the equation of the above sequence is a_{n}= 145 + 2(n-1). - Setting an to n
^{2}gives us n^{2}= 145 + 2(n-1). This is a quadratic equation. Algebraic manipulation results in:

n^{2}= 145 + 2(n-1)

n^{2}= 145 + 2n - 2

n^{2}- 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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