Question

Quantos termos tem na PA ( -3,1,5........113 )

Answer 1

$a_{2}=1\\a_{3}=5$

Achando a razão da P.A:

$r=a_{3}-a_{2}=5-1=4$
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Queremos achar 'n' tal que 'an' = 113:

$a_{n}=a_{1}+(n-1)r~~~~~~(termo~geral~da~P.A)\\113=-3+(n-1)\cdot4\\113+3=4\cdot(n-1)\\4\cdot(n-1)=116\\(n-1)=116/4\\n-1=29\\n=29+1\\\\\boxed{\boxed{n=30}}$

Logo, a P.A possui 30 termos