Question

Can I get some assistance with setting this problem up please?

Answer 1

Step 1. The sequence that we have in the table is:

`5,\text{ 10, 20, ...}`

As you can see the number doubles each time.

We require to find the expression that represents the sum for term 3 through term 9 in sigma notation.

Step 2. First, since the summation has to be from term 3 to term 9, the sigma notation should look as follows:

`\sum_{n\mathop{=}3}^9`

This discards options 1 and 3.

Step 3. Now we need to find an expression that represents the sum of the terms. If we continue the sequence the numbers would be:

`5,10,20,40,80,...`

We can also express this as 5 multiplied by a power of 2:

`5\cdot2^0+5\cdot2^1+5\cdot2^3+...`

That is because

2^0=1

2^1=2

2^2^4

.

.

.

Therefore, the result of the multiplications:

This can be simplified to:

`5(2)^(n-1)`

Step 4. The final expression is:

`\sum_{n\mathop{=}3}^95(2)^(n-1)`

Which is shown in the second option.

Answer:

`\sum_{n\mathop{=}3}^95(2)^(n-1)`