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

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The infinite sequence a_{1}, a_{2}, \dots, a_{n}, \dots is such that a_{1} = 2, a_{2} = - 3, a_{3} = 5, a_{4} = - 1, and a_{n} = a_{n -}_{4} for n > 4 . What is the sum of the first 97 terms of the sequence?

Explanation	Calculations	Help
$We note that the sequence repeats every 4 terms due to the definition of a_{n} .$	$a_{n} = a_{n - 4}$
$We find how many full 4-term cycles are contained in the first 97 terms and the number of extra terms.$	$97 \div 4 = 24 remainder 1$
$We calculate the sum of one full 4-term cycle.$	$2 + (- 3) + 5 + (- 1) = 3$
$We multiply the number of full cycles by the cycle sum to get the total from all full cycles.$	$24 \times 3 = (20 + 4) \times 3 = (20 \times 3) + (4 \times 3) = 60 + 12 = 72$	Theory & Tactics Method Card CALC2-D Click to view full details
$We add the contribution from the single extra term (the first term of the next cycle).$	$72 + 2 = 74$

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74

The infinite sequence a_{1}, a_{2}, \dots, a_{n}, \dots is such that a_{1} = 2, a_{2} = - 3, a_{3} = 5, a_{4} = - 1, and a_{n} = a_{n -}_{4} for n > 4 . What is the sum of the first 97 terms of the sequence?

Explanation	Calculations	Help
$We note that the sequence repeats every 4 terms due to the definition of a_{n} .$	$a_{n} = a_{n - 4}$
$We find how many full 4-term cycles are contained in the first 97 terms and the number of extra terms.$	$97 \div 4 = 24 remainder 1$
$We calculate the sum of one full 4-term cycle.$	$2 + (- 3) + 5 + (- 1) = 3$
$We multiply the number of full cycles by the cycle sum to get the total from all full cycles.$	$24 \times 3 = (20 + 4) \times 3 = (20 \times 3) + (4 \times 3) = 60 + 12 = 72$	Theory & Tactics Method Card CALC2-D Click to view full details
$We add the contribution from the single extra term (the first term of the next cycle).$	$72 + 2 = 74$

Scroll horizontally to view all columns

74