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Mathematics

Grade10

Easy

Question

The sum of the terms of the sequence $not stretchy sum from n equals 1 to 5 of fraction numerator 1 over denominator 2 end fraction open parentheses 3 close parentheses to the power of n minus 1 end exponent$ is _____.

3
7
$\frac{1}{2}$
8

hint Hint:

The sum of terms of a geometric progression is given by $S subscript n equals a subscript 1 fraction numerator open parentheses r to the power of n minus 1 close parentheses over denominator open parentheses r minus 1 close parentheses end fraction$

The correct answer is: 8

The sum of terms of the sequence $not stretchy sum from n equals 1 to 5 of fraction numerator 1 over denominator 2 end fraction open parentheses 3 close parentheses to the power of n minus 1 end exponent$ is $S subscript n equals a subscript 1 fraction numerator open parentheses r to the power of n minus 1 close parentheses over denominator open parentheses r minus 1 close parentheses end fraction$
$S subscript n equals a subscript 1 fraction numerator open parentheses r to the power of n minus 1 close parentheses over denominator open parentheses r minus 1 close parentheses end fraction$ = $1 half cross times fraction numerator 3 to the power of 5 minus 1 over denominator 3 minus 1 end fraction$

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