Sum of the First n Terms of a Geometric Sequence
Given a geometric sequence (or series) with a first-term a1 and common ratio r, the sum of the first n terms is given by:
We are given the series:
Before calculating the required sum, we need to find the common ratio. It's defined as the division of two consecutive terms. For example, using the first two terms:
The first term is a1 =120. Now apply the formula:
Operating:
Calculating:
Answer:
The answer to your question is: 6x² + 8x.
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Let x be the number of pounds of beans that sells for $0.72 used and y
be the number of pounds of beans that sells for $0.52 used. Then:
x + y = 110 . . . (1)
0.72x + 0.52y = 81.4 . . . (2)
From (1), x = 110 - y . . . (3)
Putting (3) into (2) gives
0.72(110 - y) + 0.52y = 81.4
79.2 - 0.72y + 0.52y = 81.4
79.2 - 0.2y = 81.4
0.2y = 79.2 - 81.4 = -2.2
y = -2.2/0.2 = -11
x = 110 - (-11) = 110 + 11 = 121
The solution is not reasonable because, there cannot be negative value for the number of pounds of beans used.
And 121 pounds of beans cannot produce 110 pounds.