What is the answer to x-5?
2 answers:
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Answer:
The first three terms of the geometry sequence would be ,
, and
.
The sum of the first seven terms of the geometric sequence would be .
Step-by-step explanation:
<h3>1.</h3>Let denote the common difference of the arithmetic sequence.
Let 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
.
The question states that the first term of this arithmetic sequence is . Hence:
- The third term of this arithmetic sequence would be
.
- The thirteenth term of would be
.
The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let denote the ratio of the geometric sequence in this question.
Ratio between the second term and the first term of the geometric sequence:
.
Ratio between the third term and the second term of the geometric sequence:
.
Both and
are expressions for
, the common ratio of this geometric sequence. Hence, equate these two expressions and solve for
, the common difference of this arithmetic sequence.
.
.
.
Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be ,
, and
, respectively.
These three terms (,
, and
, respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be
.
Let and
denote the first term and the common ratio of a geometric sequence. The sum of the first
terms would be:
.
For the geometric sequence in this question, and
.
Hence, the sum of the first terms of this geometric sequence would be:
.