Give the first five terms of the geometric sequence. 𝑎1=−972,𝑎𝑛=−1/3𝑎𝑛−1

Answer 1

Give the first five terms of the geometric sequence. 𝑎₁=−972

𝑎_𝑛=−(1/3)𝑎_𝑛−1 for n>1

Answer 2

an = -1/3an-1 or an=-(1/3)(an-1)? if the 1st then

a0 = 1/2916

a1 = -1/3a0 = -1/3(1/2916) = --972

a2 =-1/3(a1) -1/3(-972) = 1/2916

a3 = -1/8748

a4 = 1/26244

a5 = -1/78732

unless you really meant to write

an = (1/3)a(n-1) not an = 1/(3an-1)

then

a0 = 2916

a1 = -(1/3)a0 = = -(1/3)2916 = -972

a2 = -(1/3)(-972) = 324

a3 -(1/3)324 = - 108

a4 = -(1/3)(-108) = 36

a5 = -(1/3)36) = - 6

Odds are you meant the latter

Answer 3

Izabel, a geometric series has terms that are connected by constant multiplication. For example, 10, -20, 40, -80...

My series above has a₁= 10 and r = -2. We could say the third term is found by multiplying the second term by -2 which can be expressed as a₃= a₂ r or a_n= a_n-1r or a_n-1(-2)

Where you see "n," that refers to where the term appears a₀ can be the first term, but it is also possible to have a₁ be the first term--that part is relative.

For your question, we have a_n which refers to any general term and we are told that it equals negative one-third times the previous term. Term 5 is negative one-third times term 4, for example. I hope this helps, but please let me know--Andrew