Question

qual o numero de termos da PA (-3,1,5....113?

Answer 1

an = 113
a1 = -3
r = 4
n = ?

an = a1 + (n - 1)r
113 = -3 + (n - 1)4
113 = -3 + 4n - 4
4n = -7 - 113
4n = 120
n = 120/4
n = 30

(-3 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113)

BONS ESTUDOS

Answer 2

$a_{1}=-3\\ \\ a_{n}=113\\ \\ r=1-\left(-3 \right ) \Rightarrow r=4\\ \\ \\ a_{n}=a_{1}+\left(n-1 \right )\cdot r\\ \\ 113=-3+\left(n-1 \right )\cdot 4\\ \\ 4\left(n-1 \right )=113+3\\ \\ 4\left(n-1 \right )=116\\ \\ n-1=\dfrac{116}{4}\\ \\ n-1=29\\ \\ n=29+1\\ \\ \boxed{n=30 \text{ termos}}$