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.

3 0

4 years ago