Question

FOR PROBLEMS 1 AND 2. Use the sequence formulas. Carry out your calculations to the final number. Round the results to 1 decimal place.   
1. Consider the sequence: 1/2, 1, 2, 4, 8, a. Find the 30th term of the sequence.
b. Find the sum of the first 30 terms of the sequence.

2. You give your daughter a piggy bank with $2 in it. She puts $5 in it the next week and each week thereafter. How much money will she have in it after 24 weeks. (i.e. we are asking for a24)


FOR PROBLEMS 3,4, and 5: Paste a screen shot of your program files and your IDLE output into your HW PDF.

3. There are six items to be rung up in the cash register. The first item costs $15.00. Each item after that costs an additional $2.00. (item #2 costs $17, item #3 costs $19, etc.)
Create Python program code using a for loop that will print the cost of each item, starting with the $15 item, and it will calculate and print the total cost. Your program should then use the sequence formula as an alternative way to calculate the total cost and print the result.

Answer 1

1) This is a Geometric Progression series and the 30th term will be a*r(30-1) , where a = 0.5 and r = 2

So, the 30th term will be 0.5*229 = 26,84,35,456

The sum of the first 30 terms = 0.5*(230-1) / (2-1)

= 53,68,70,912.

2) This is a case of arithmetic Progression.

where a = 2, d = 5 and n = 24.

We need find the money after 24 weeks.

a24 = a + (n-1) * d

a24 = 2+23*5

a24 = 117.

So, the money in the piggy bank after 24th week is $117.

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