Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 - n, where a0 = 4.

Question

Mathematics

Jolie Harvey

26 August, 08:23

Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 - n, where a0 = 4.

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Answers (1)

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Karson Henson · Answer 1

The closed formula for an = an-1 - n will be found using the formula for arithmetic sequence given by:

an=a+d (n-1)

where

a=first term

d=common difference

n=number of terms

From the formula given:

a=4

d=n

thus the formula will be:

an=a+n (n-1)

an=4+n (n-1)