The sequence a_{1}, a_{2}, \ldots a_{n}, \ldots is... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

GMAT Quant — Algebra (Linear Equations)

The sequence a_{1}, a_{2}, \dots a_{n}, \dots is such that a_{n} = 2 a_{n - 1} - x for all positive integers n \geq 2 and for a certain number x . If a_{5} = 99 and a_{3} = 27, what is the value of x ?

Explanation	Calculations	Help
$We use the recurrence \textbf{" = 2 - x"} and the given values \textbf{" = 27"} and \textbf{" = 99"} to express the fifth term in terms of the third term and x by stepping forward from index 3 to index 5.$	$a_{4} = 2 a_{3} - x a_{4} = 2 \times 27 - x a_{4} = 54 - x a_{5} = 2 a_{4} - x a_{5} = 2 \times (54 - x) - x a_{5} = 108 - 3 x$
$We set this expression for the fifth term equal to the given value \textbf{" = 99"} and solve for x.$	$108 - 3 x = 99 - 3 x = 99 - 108 - 3 x = - 9 x = \frac{- 9}{- 3} x = 3$	Theory & Tactics Method Card EQUA1-B Click to view full details Theory & Tactics Method Card EQUA1-C Click to view full details

Scroll horizontally to view all columns

3

GMAT Quant — Algebra (Linear Equations)

The sequence a_{1}, a_{2}, \dots a_{n}, \dots is such that a_{n} = 2 a_{n - 1} - x for all positive integers n \geq 2 and for a certain number x . If a_{5} = 99 and a_{3} = 27, what is the value of x ?

Explanation	Calculations	Help
$We use the recurrence \textbf{" = 2 - x"} and the given values \textbf{" = 27"} and \textbf{" = 99"} to express the fifth term in terms of the third term and x by stepping forward from index 3 to index 5.$	$a_{4} = 2 a_{3} - x a_{4} = 2 \times 27 - x a_{4} = 54 - x a_{5} = 2 a_{4} - x a_{5} = 2 \times (54 - x) - x a_{5} = 108 - 3 x$
$We set this expression for the fifth term equal to the given value \textbf{" = 99"} and solve for x.$	$108 - 3 x = 99 - 3 x = 99 - 108 - 3 x = - 9 x = \frac{- 9}{- 3} x = 3$	Theory & Tactics Method Card EQUA1-B Click to view full details Theory & Tactics Method Card EQUA1-C Click to view full details

Scroll horizontally to view all columns

3