Question
3.1 The
term of an arithmetic sequence is -3 and the
term is -35 .
Determine the common difference and the first term.
3.2 Evaluate :
3.3 The following sequence forms a convergent geometric sequence:
Determine the possible values of x .
3.3 .2 If
, calculate
.
Determine the common difference and the first term.
3.2 Evaluate :
3.3 The following sequence forms a convergent geometric sequence:
3.3 .2 If
Ask by Valdez Johnson. in South Africa
Jan 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
-
3.1
- First term: 3
- Common difference: -2
-
3.2
-
3.3.1
-
3.3.2
Solution

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Beyond the Answer
To find the common difference and the first term of the arithmetic sequence, you can use the formula for the
-th term,
. Set up two equations based on the
term (-3) and the
term (-35). Solving these yields
and
.
In the geometric sequence, to ensure convergence, the absolute value of the ratio needs to be less than 1. Here, you can analyze each term in relation to
and derive
to find the valid range for
. This means
.