Question

Encontre o valor de m, sabendo que a sequência (1, m - 1, 3m + m²) é uma PG.

Answer 1

$\displaystyle \text{PG}\to (1, \text m-1,3\text m+\text m^2) \\\\ \underline{\text{Propriedade da PG}}:\\\\ (\text A_2)^2 = \text{A}_1.\text{A}_3 \\\\ (\text m-1)^2=1.(3\text m+\text m ^2) \\\\ \text m^2-2\text m+1=3\text m+\text m^2 \\\\ 3\text m+2\text m= 1 \\\\ 5\text m = 1 \\\\ \huge\boxed{\text m = \frac{1}{5}\ }\checkmark$