Which quantity is greater? (2)

Algebra Level 3

In the sequence a 1 , a 2 , a 3 , , a n , , a_1,a_2,a_3,\dots,a_n,\dots, and a 1 = 4 a_1=4 and each term after the first term is equal to the preceding term plus 6. 6.

In the sequence b 1 , b 2 , b 3 , , b n , , b_1,b_2,b_3,\dots,b_n,\dots, the n t h n^{th} term of the sequence is given by the formula b n = 2 n 1 b_n=2^{n-1}

Quantity A: a 43 a_{43}

Quantity B: b 9 b_9

A < B A< B A > B A > B A = B A = B The realtionship can not be determined

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1 solution

Chan Tin Ping
Dec 30, 2017

Sequence a n {a_{n}} is arithmetic progression, so a 43 = 4 + ( 43 1 ) × 6 = 256 a_{43}=4+(43-1)×6=256 . While b 9 = 2 9 1 = 25 b_{9}=2^{9-1}=25 .

Hence a 43 = 256 = b 9 a_{43}=256=b_{9} , so A = B \large A=B .

Nice solution. Thank you for sharing it.

Hana Wehbi - 3 years, 5 months ago

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You are welcome. 😊

Chan Tin Ping - 3 years, 5 months ago

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