In a geometric sequence the 3rd term is 24 and the 8th term is 768. Use the form

Question

In a geometric sequence the 3rd term is 24 and the 8th term is 768.

Use the formula to calculate the 20th term.

Use the formula to calculate the sum of the 20 terms.

Check your answers above by writing a Python program to calculate and print each of the 20 terms of the sequence.

Your program should use a for loop to calculate the terms and also to calculate the sum of the 20 terms.

It should then calculate the value of the sum that is generated by using the formula for the sum of a geometric sequence.

The program should compare the two sums and print both sums and your conclusion.

Paste a screenshot of the Python code and the output.

Explanation / Answer

''' 24=a*r^2 768=a*r^7 r^5=768/24=32 r=2 a=6 ''' a=6 r=2 Total=0 for i in range(20): print('Term',i+1,' : ',a) Total+=a a=a*r SumFormula=6*(2**20-1)/1 print('Sum using for loop:',Total) print('Sum using formula:',SumFormula)

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