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GMAT Quant — Quant (Patterns)

The infinite sequence b_{1}, b_{2}, \dots, b_{n}, \dots is such that b_{1} = 4, b_{2} = - 2, b_{3} = 3, b_{4} = 1, and b_{n} = b_{n - 4} for n > 4 . What is the sum of the first 103 terms of the sequence?

Explanation	Calculations	Help
$We note that the sequence repeats every 4 terms by the given definition.$	$b_{n} = b_{n - 4}$
$We determine how many full 4-term cycles fit in the first 103 terms and the remaining terms.$	$103 \div 4 = 25 remainder 3$
$We calculate the sum of one full 4-term cycle.$	$4 + (- 2) + 3 + 1 = 6$
$We multiply the number of full cycles by the cycle sum to get the total from all full cycles.$	$25 \times 6 = (20 + 5) \times 6 = (20 \times 6) + (5 \times 6) = 120 + 30 = 150$	Theory & Tactics Method Card CALC2-D Click to view full details
$We add the contribution from the extra 3 terms (the first three terms of the next cycle).$	$150 + (4 + (- 2) + 3) = 150 + 5 = 155$

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B

GMAT Quant — Quant (Patterns)

The infinite sequence b_{1}, b_{2}, \dots, b_{n}, \dots is such that b_{1} = 4, b_{2} = - 2, b_{3} = 3, b_{4} = 1, and b_{n} = b_{n - 4} for n > 4 . What is the sum of the first 103 terms of the sequence?

Explanation	Calculations	Help
$We note that the sequence repeats every 4 terms by the given definition.$	$b_{n} = b_{n - 4}$
$We determine how many full 4-term cycles fit in the first 103 terms and the remaining terms.$	$103 \div 4 = 25 remainder 3$
$We calculate the sum of one full 4-term cycle.$	$4 + (- 2) + 3 + 1 = 6$
$We multiply the number of full cycles by the cycle sum to get the total from all full cycles.$	$25 \times 6 = (20 + 5) \times 6 = (20 \times 6) + (5 \times 6) = 120 + 30 = 150$	Theory & Tactics Method Card CALC2-D Click to view full details
$We add the contribution from the extra 3 terms (the first three terms of the next cycle).$	$150 + (4 + (- 2) + 3) = 150 + 5 = 155$

Scroll horizontally to view all columns

B