1. What is the amount of the geometric series 8,– 16, 32 … if there are 15 terms? (1 point).
= 8 [( -2 )^ 15 -1]/ [( -2 )-1]= 87384.
2. What is the amount of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point).
= 4( 3 ^ 9 – 1)/( 3 – 1).
= 39364.
3. What is the amount of a 6-term geometric sequence if the very first term is 11, the last term is– 11,264 and the common ratio is– 4? (1 point).
= -11 (1-( -4 ^ n))/( 1-( -4 )).
= 11( 1-( -11264/ 11))/( 1-( -4 )).
= 2255.
4. What is the sum of an 8-term geometric series if the first term is 10 and the last term is 781,250? (1 point).
= 8 (1-390625)/( 1-5).
= 781,248.
For issues 5 8, identify whether the issue should be solved utilizing the formula for an arithmetic sequence, math series, geometric series, or geometric series. Explain your answer in complete sentences. You do not require to fix. 5. Jackie deposited $5 into a checking account in February. For each month following, the deposit amount was doubled. Just how much cash was transferred in the bank account in the month of August? (1 point).
To solve this, a geometric series is utilized because the terms share a consistent ratio as 2.
6. A local supermarket stacks the soup cans in such a way that each row has 2 fewer cans than the row listed below it. If there are 32 cans on the bottom row, how many overall cans are on the bottom 14 rows? (1 point).
To resolve you use a formula for an arithmetic series since for every row, the number of cans keep reducing.
7. A major US city reports a 12% increase in decoration sales during the yearly holiday season. If decoration sales were 8 million in 1998, how much did the city report in total decoration sales by the end of 2004?(1 point)
You would use a geometric series formula because the increase will be different each year because the percentage increase affects the outcome of the next years by a common ratio.
8. A fireplace contains 46 bricks along its bottom row. If each row above decreases by 4 bricks, how many bricks are on the 12th row? (1 point) To solve you have to use the formula for an arithmetic sequence because the amount of decrease remains the same and the ratio between the set of numbers stays the same.
9. Using complete sentences, explain the difference between an exponential function and a geometric series.(2 points) An exponential function is continuous. A geometric series is discrete.
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