The first 9 terms of a sequence are 8, 7, 5, 1, -7, -23, -55, -119, -247. Which recursive formula could have been used to produce these terms?

Question

the homework is about arithmetic sequences.

Answer 1

the first term of the sequence is 8

consider another sequence starting from 1 and the next term is the double of the previous one.

so this sequence is as follows: 1, 2, 4, 8, 16, 32.............

we subdract from the first term of the first sequence the first term of the second one, from the second term the second one and so on.

In this way we will have 8-1=7.   7-2=5.  5-4=1  1-8=-7 and so on

 

 

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