Question

5. A soma dos 6 primeiros termos da PA (1.5, ...) é: *
(A) 58
O (B) 40
O (C) 50
O (D) 66
O (E) 32​

Answer 1

D) 66

Explicação passo-a-passo:

primeiro temos que encontrar o valor da razão dessa P.A

r = a2 - a1

r = 5 - 1

r = 4

agora temos que encontrar o valor de a6.

$</strong><strong>a_</strong><strong>{n} = a1 + (n - 1) \times r \\ </strong><strong>a_</strong><strong>{6} = 1 + (6 - 1) \times 4 \\ </strong><strong>a_</strong><strong>{6} = 1 + 5 \times 4 \\ </strong><strong>a_</strong><strong>{6} = 1 + 20 \\ </strong><strong>a_</strong><strong>{6} = 21$

agora sabemos o valor de a6 iremos encontrar a soma dos 6 primeiros termos dessa P.A

$</strong><strong>s_</strong><strong>{n} = \frac{(a1 + an) \times n}{2} \\ </strong><strong>s_</strong><strong>{6} = \frac{(1 + 21) \times </strong><strong>6</strong><strong>}{2 } \\s </strong><strong>_</strong><strong>{6} = \frac{22 \times </strong><strong>6</strong><strong>}{2} \\ </strong><strong>s_</strong><strong>{6} = \frac{</strong><strong>1</strong><strong>3</strong><strong>2</strong><strong>}{2} \\ \red{ \boxed{ \boxed{ \boxed{ </strong><strong>s_</strong><strong>{6} = </strong><strong>6</strong><strong>6</strong><strong>}}}}$

espero ter ajudado :)