Answer:
Least to greatest: Left, 2nd from Left, Right, Second from Right.
Least to greatest numerically: 31,80,121,127
Step-by-step explanation:
All of these can either be done manually or by using the geometric series formula. I'll do a couple each way.
Left: Manual
3(1 + 2 + 4 + 8 + 16) = 3*31 = 93
Sample Calculation
- Three is a common factor; there is no point in calculating it for every term.
- Pull it out as a common factor.
- For i = 4
- 2^(4 - 1) = 2^3 = 8 which is what the series shows.
Second from the Left Manual
2(1 + 3 + 9 + 27) = 2 (40) = 80
Sample Calculation
- Two is a common factor; there is no point in calculating it every time.
- Pull it out as a common factor
- For i = 4
- 3^(4 - 1) = 3^3 = 27 which is what the series shows.
Second from the Right
Givens
- a1 = 1 [See sample above]
- n = 7
- r = 2
Formula
Sum = a(1 - r^n)/(1 - r)
Solution
- Sum = 1(1 - 2^7)/(1 - 2)
- Sum = 1(1 - 128)/(-1)
- Sum = 1*(-127)/-1
- Sum = 127
Right hand Side
Givens
Formula
Sum = a(1 - r^n)/(1 - r)
Solution
- Sum = 1(1 - 3^5)/(1 - 3)
- Sum = 1(1 - 243)/-2
- Sum = (-242)/-2
- Sum = 121
