What is the first term of the geometric sequence presented in the table below?

n49

an−35185,293

Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.

a1 = 13

a1 = 3

a1= -1/3

a1 = −13

Not D

failurewithasmile
Apr 14, 2017

#1**0 **

n 4 9

an −351 85,293

Hopefully that makes more sense of a chart lol.....

failurewithasmile
Apr 14, 2017

#3**+2 **

We have that

-351 = a_{1} (r)^(4 - 1)

-351 = a_{1} (r)^3 divide both sides by r^(3)

-351/ r^3 = a_{1} (1)

And

85293 = a1 (r)^(9 -1)

85293 = a1 (r)^8 sub (1) into this

85293 = [ -351/r^3] r^8

85293 = -351 r^5 divide both sides by -351

-243 = r^5 take the 5th root of both sides

(-243)^(1/5) = r = - 3

Using (1)

-351 / (-3)^3 = -351 / -27 = a_{1} = 13

CPhill
Apr 15, 2017