Respuesta :
This is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.
How to find the first five terms of sequence a₁ = -2, a (n) =a (n-1)-5 ?
A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formulas:
1. The initial term in the series.
2. The general rule for determining any term from its preceding term.
Recursive Arithmetic Sequence Formula
The following is the recursive formula to determine the nth term in an arithmetic series:
an = an-1 + d for n ≥ 2
where
The common difference is d, and an is the nth term of an A.P.
given that
a₁ = -2
a (n) =a (n-1) -5 so, d = -5
For example, we need to extend the sequence term by term in order to find the first five terms:
a(1) = -2
a(2) = a(1) + d = -2 + (-5) = -7
a(3) = a(2) + d = -7 + (-5) = -12
a(4) = a(3) + d = -12 + (-5) = -17
a(5) = a(4) + d = -17 + (-5) = -22
a(6) = a(5) + d = -22 + (-5) = -27
Hence,this is recursive sequence and -2, -7, -12, -17, -22, -37 these are the first five terms of sequence.
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