## an arithmetic sequence “a” starts with 84, 77 define “a” recursively

Question

an arithmetic sequence “a” starts with 84, 77 define “a” recursively

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1 month 2021-08-04T08:25:44+00:00 1 Answers 8 views 0

## Answers ( )

First, let’s define an arithmetic sequence:

In an arithmetic sequence, the difference between any two consecutive terms is always the same.

Then we can write it in a general way as:

aₙ = a₁ + (n – 1)*d

where:

aₙ is the n-th term of the sequence.

d is the constant difference between two consecutive terms.

a₁ is the initial term of our sequence.

Now in this case we know that the first terms of our sequence are:

84, 77, …

Then we know the initial term of our sequence:

a₁ = 84.

And the value of d can be calculated as:

d = a₂ – a₁ = 77 – 84 = -7

Then the general way of writing this sequence is:

aₙ = 84 + (n – 1)*(-7)

And the recursion relation is:

aₙ = aₙ₋₁ – 7

So for the n-th term, we must subtract 7 of the previous term.