Question

Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmetic or geometric? Explain your answer.

Answer 1

Hello,

This sequence is geometric with a ratio of -3

the first term is 6

Explanation:

`u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_(n+1)=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _(i=1)u_i = \lim_(n \to \infty) \sum\limits^n _(i=1)u_1*(-3)^(i-1)\\=6*\lim_(n \to \infty) \sum\limits^\infty _(i=1)(-3)^(i-1)\\=6*(1-(-3)^n)/(1-(-3)) \\=(3)/(2) *({1-(-3)^n)\\`

serie does not converge.