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Mathematics

Grade10

Easy

Question

Find the first term of the sequence given by $S subscript n end subscript equals 5 open parentheses fraction numerator 1 minus open parentheses fraction numerator 2 over denominator 3 end fraction close parentheses to the power of n end exponent over denominator fraction numerator 1 over denominator 3 end fraction end fraction close parentheses$ .

$\frac{1}{3}$
$\frac{3}{2}$
5
6

hint Hint:

The sum of n terms of a geometric sequence is given by $S subscript n end subscript equals fraction numerator a subscript 1 end subscript open parentheses 1 minus r to the power of n end exponent close parentheses over denominator left parenthesis 1 minus r right parenthesis end fraction$ , where $a subscript 1 end subscript$ is the first term and $r$ is the common ratio and $n$ is the number of terms.

The correct answer is: 5

The sum of n terms of a geometric sequence is given by $S subscript n end subscript equals fraction numerator a subscript 1 end subscript open parentheses 1 minus r to the power of n end exponent close parentheses over denominator left parenthesis 1 minus r right parenthesis end fraction$ , where $a subscript 1 end subscript$ is the first term and $r$ is the common ratio and $n$ is the number of terms.
The first term of the sequence is 5.

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