Question

Encontre a P.A tal que a soma dos n primeiros é n ao quadrado

Answer 1

Resposta:

PA(1, 3, 5, 7, 9, ...)

Explicação passo a passo:

$S_n=n^2\\\\p/n=1 \impliesS_1=1^2=1 \implies a_1=1\\\\p/n=2 \implies S_2=2^2=4 \implies a_1+a_2=4 \implies 1+a_2=4 \implies a_2=3\\\\p/n=3 \implies S_3=3^2=9 \implies a_1+a_2+a_3=9 \implies 1+3+a_3=9 \ \implies\\\\ a_3=9-1-3=5\\\\PA(1,3,5,7,9,...)$