Mathematics, 17.03.2021 23:50, aaliyahlopez85
The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term of both sequences is 1, determine:
1.) the first three terms of the geometric sequence if r > 1
2.) the sum of 7 terms of the geometric sequence if the sequence is 1, 5, 25
Answers: 3
, 
, and 
.
. 
denote the common difference of the arithmetic sequence. 
denote the first term of the arithmetic sequence. The expression for the 
th term of this sequence (where 
is a positive whole number) would be 
.
. Hence:
. The thirteenth term of would be 
.
denote the ratio of the geometric sequence in this question.
.
.
and 
are expressions for 
.
.
.
, and 
, respectively.
.
.
.
terms of this geometric sequence would be:
.
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