Answer:
26042.
Step-by-step explanation:
What's the first term of this geometric series?
2.
What's the common ratio of this geometric series?
Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2.
.
What's the sum of this series to the seventh term?
The sum of the first n terms of a geometric series is:
,
where
.
The greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).
<h3>What is a sequence?</h3>It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The total length of the wood = 90 in
We have to cut it into the greatest number of pieces, where each piece will have a different length and the length of each piece is a whole number, in inches.
We can cut it like:
1 in, 2 in, 3 in, 4 in, and so on
The above shows the arithmetic sequence,
The sum of the n natural number is given by:
After solving, we will get a quadratic equation:
n² + n -180 = 0
After solving, we will get:
n = 12.92 and n = -13.92(term can not be negative)
n = 12 (taking whole number)
Thus, the greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).
Learn more about the sequence here:
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