Question

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

Answer 1

Answer:

Option C.

Step-by-step explanation:

The given expression is $\sum_{r=1}^{r=3}[4\times (\frac{1}{2})^{(r-1)}]$

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 = $\frac{1}{2}$

Sum of a geometric sequence is represented by the expression,

$S_{n}=\frac{a(1-r^{n})}{1-r}$

$S_{3}=\frac{4(1-\frac{1}{2})^{3}}{(1-\frac{1}{2})}$

$S_{3}=\frac{4(1-\frac{1}{8})}{(1-\frac{1}{2})}$

$S_{3}=\frac{4(\frac{7}{8})}{\frac{1}{2} }$

$S_{3}=7$

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