# Arithmetic progression

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1. What is the amount of the geometric sequence 8,– 16, 32 … if there are 15 terms? (1 point).

= eight [( -2 )^ 15 -1]/ [( -2 )-1]= 87384.

2. What is the quantity of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point).

= 4( three ^ 9 – 1)/( three – 1).

= 39364.

3. What is the quantity of a 6-term geometric sequence if the very first term is eleven, the last time period is– eleven,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 primary time period is 10 and the final time period is 781,250? (1 point).

= eight (1-390625)/( 1-5).

= 781,248.

For points 5 eight, determine whether or not the problem ought to be solved utilizing the formula for an arithmetic sequence, math series, geometric collection, or geometric series. Explain your reply in full sentences. You do not require to repair. 5. Jackie deposited $5 right into a checking account in February. For every month following, the deposit amount was doubled. Just how much money was transferred in the checking account in the month of August? (1 point).

To solve this, a geometrical series is utilized because the terms share a constant ratio as 2.

6. A local grocery store stacks the soup cans in such a way that each row has 2 fewer cans than the row listed under it. If there are 32 cans on the bottom row, what quantity of total cans are on the bottom 14 rows? (1 point).

To resolve you utilize a formulation for an arithmetic sequence since for every row, the number of cans hold lowering.

7. A major US city stories a 12% increase in ornament gross sales through the yearly holiday season. If ornament gross sales were eight million in 1998, how much did the town report in whole decoration gross sales by the end of 2004?(1 point)

You would use a geometric series method as a outcome of the rise shall be totally different every year because the percentage improve impacts the outcome of the following years by a typical ratio.

8. A hearth contains 46 bricks alongside its bottom row. If each row above decreases by 4 bricks, how many bricks are on the 12th row? (1 point) To clear up you must use the method for an arithmetic sequence because the quantity of lower stays the identical and the ratio between the set of numbers stays the same.

9. Using full sentences, clarify the distinction between an exponential perform and a geometrical collection.(2 points) An exponential perform is steady. A geometric series is discrete.