2) Write the general formula for n-th element of the following sequence: 1/2, 4/5, 4/3, 16/7, 4, 64/9?

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Answer 1 · 2018-03-18T13:46:13

#a_n = 2^n/(n+3)#

Given:

#1/2, 4/5, 4/3, 16/7, 4, 64/9#

We can given these terms denominators in ascending sequence to get:

#2/4, 4/5, 8/6, 16/7, 32/8, 64/9#

Note that the numerators are successive powers of #2#.

Hence we can write a formula:

#a_n = 2^n/(n+3)#