I don't know exactly how to label these. I'll start from the left and go to the right. The formula for all of these questions is Sum = a(1 - r^n)/(1 - r)
Left
The complete series is 1 3 9 27 81 and just adding these as you see them, you get 1 + 3 + 9 + 27 + 81 = 121
Sample calculation
i = 1
3^(1 -1) = 1
i = 4
1 * 3^(4 - 1)=3^3 = 27 Just what the series says you should get.
Sum using formula
Sum = 1(1 - 3^5)/(1 - 3) = 1 * (1 - 243)/(1 - 3) = - 242/-2 = 121
Second from the left
Series: 3 6 12 24 48
Sum by hand = 93
Sample Calculation
i = 1
3*2^(1 - 1) = 1
i1 = 3
3 * 2^(3 - 1) = 3 * 2^2 = 3 * 4 = 12 which is what you should get.
Sum using formula
Sum = 3 (1 - 2^(5 - 1) / (1 - 2)
Sum = 3 (1 - 32) / - 1
Sum = 3(-31) / (- 1) = 93
Second from the right.
Series: 2 6 18 54
Sample Calculation
i = 1
t1 = 2* 3^(1 - 1) = 2*3^0 = 2*1 = 2
i = 4
t4 = 2 * 3^(4- 1)
t4 = 2 * 3^3
t4 = 2 * 27
t4 = 54 just as it should
Sum with formula
Sum = 2( 1 - 3^4) / ( 1 - 3)
Sum = 2(1 - 81)/ -2
Sum = 2( - 80) / - 2
Sum = 80
Entry on the right
Series: 1 2 4 8 16 32 64
Sum by hand: 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127
Sample Calculation:
i = 1
2^(1 - 1) = 2^0
2 to the zero = 1
i = 6
t6 = 1( 2^6)
t6 = 1 * 2^6 = 64
Sum using the formula: 1*(1 - 2^7)/(1 - 2) = (1 - 128)/(-1 = 127
Order: Answer
Right comes first
Left
Second from the left
Second from the right.
