Question

Select the correct answer.
what is the value of (4 x (1/2)-1).
What is the value of t=1​

Answer 1

Option C.

Explanation:

The given expression is
`\sum_(r=1)^(r=3)[4* ((1)/(2))^((r-1))]`

We have to find the sum of 3 terms of the sequence formed.

The given sequence is a geometric sequence.

Explicit formula for this sequence is in the form of

`T_(n)=ar^(n-1)`

In the given formula first term a = 4

and common ratio r =
`(1)/(2)`

Sum of a geometric sequence is represented by the expression,

`S_(n)=(a(1-r^(n)))/(1-r)`

`S_(3)=(4(1-(1)/(2))^(3))/((1-(1)/(2)))`

`S_(3)=(4(1-(1)/(8)))/((1-(1)/(2)))`

`S_(3)=(4((7)/(8)))/((1)/(2) )`

`S_(3)=7`

Therefore, Option C is the answer.

Answer 2

For this case we must substitute the values t = 1,2,3 in the given series:

For
`t = 1:`

`4 * (\frac {1} {2}) ^ {t-1} = 4 * (\frac {1} {2}) ^ {1-1} = 4 * (\frac {1} {2})^(0) = 4 * 1 = 4`

For
`t = 2`:

`4 * (\frac {1} {2}) ^ {t-1} = 4 * (\frac {1} {2})^(2-1) = 4 * (\frac {1} {2})^(1) = 4 * \frac {1} {2} = 2`

For
`t = 3`:
`4 * (\frac {1} {2}) ^ {t-1} = 4 * (\frac {1} {2})^(3-1) = 4 * (\frac {1} {2})^2 = 4 * \frac {1} {4} = 1`

We add:

`4 + 2 + 1 = 7`

So, the value is 7.

Answer:

Option C