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

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The infinite sequence b_{1}, b_{2}, \dots, b_{n}, \dots is defined by b_{1} = 4, b_{2} = - 2, b_{3} = 7, b_{4} = 1, and b_{n} = b_{n - 4} for n > 4 . What is the sum of the first 89 terms of this sequence?

Explanation	Calculations	Help
$We note that the sequence repeats every 4 terms due to the definition of b_{n} .$	$b_{n} = b_{n - 4}$
$We find how many full 4-term cycles are contained in the first 89 terms and the number of extra terms.$	$89 \div 4 = 22 remainder 1$
$We calculate the sum of one full 4-term cycle.$	$4 + (- 2) + 7 + 1 = 10$
$We multiply the number of full cycles by the cycle sum to get the total from all full cycles.$	$22 \times 10 = (20 + 2) \times 10 = (20 \times 10) + (2 \times 10) = 200 + 20 = 220$	Theory & Tactics Method Card CALC2-D Click to view full details
$We add the contribution from the single extra term (the first term of the next cycle).$	$220 + 4 = 224$

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C

The infinite sequence b_{1}, b_{2}, \dots, b_{n}, \dots is defined by b_{1} = 4, b_{2} = - 2, b_{3} = 7, b_{4} = 1, and b_{n} = b_{n - 4} for n > 4 . What is the sum of the first 89 terms of this sequence?

Explanation	Calculations	Help
$We note that the sequence repeats every 4 terms due to the definition of b_{n} .$	$b_{n} = b_{n - 4}$
$We find how many full 4-term cycles are contained in the first 89 terms and the number of extra terms.$	$89 \div 4 = 22 remainder 1$
$We calculate the sum of one full 4-term cycle.$	$4 + (- 2) + 7 + 1 = 10$
$We multiply the number of full cycles by the cycle sum to get the total from all full cycles.$	$22 \times 10 = (20 + 2) \times 10 = (20 \times 10) + (2 \times 10) = 200 + 20 = 220$	Theory & Tactics Method Card CALC2-D Click to view full details
$We add the contribution from the single extra term (the first term of the next cycle).$	$220 + 4 = 224$

Scroll horizontally to view all columns

C