Question 88472
The answer is 65,534
.
The sum of the terms in a geometric sequence (S) is given by the equation:
.
{{{S = a(1-r^n)/(1-r)}}}
.
in which a is the first term, r is the ratio between terms, and n is the number of terms.
In this problem a = 2, r = 2, and n = 15. Substituting these values into the equation
leads to:
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{{{S = 2(1-2^15)/(1-2)}}}
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A calculator will tell you that 2^15 = 32,768. Substituting this into the equation results in:
.
{{{S = 2(1-32768)/(1-2)}}}
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Simplify the terms that are inside the parentheses to get:
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{{{S = 2(-32767)/(-1)}}}
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Do the multiplication in the numerator:
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{{{S = -65534/-1}}}
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and the division by -1 results in:
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{{{S = 65534}}}
.
Hope this helps you see how to use the equation for the sum of the terms in a geometric
progression.