Consider this sequence: -81, -54, -36, -24, … . The sequence is . The common ratio of the sequence is . The sum of the first fiv

Question

kozerog [31]

3 years ago

8

Consider this sequence: -81, -54, -36, -24, … . The sequence is . The common ratio of the sequence is . The sum of the first fiv

e terms of the sequence is

Mathematics

2 answers:

Alinara [238K] · Answer 1 · 2022-02-10T10:51:33+03:00

Alinara [238K]3 years ago

8 0

A1 = - 81, a2 = - 54, a3 = - 36, a4 = - 24,...
The sequence is geometric sequence.
r = a2/a1 = (-54)/(-81) = 2/3
The common rate of the sequence is 2/3.
The sum of the first 5 terms:
S 5 = a1* (1-(2/3)^5) / (1-2/3) =
= 81 * ( 1- 32/243)/ (1/3) =
= 81 * ( 211*81 ) = 211

hichkok12 [17] · Answer 2 · 2022-02-10T09:41:48+03:00

hichkok12 [17]3 years ago

3 0

We have the following remark
-81/-54= -54/-36 = -36/ -24=...= 1.5
the sequence is geometric sequence
the common ratio of the sequence is 1.5
the sum of the five terms of the sequence is
S5= a[1- (1.5)^5 / 1-1.5], a first term,
S5= -42*6.5= - 276