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Eduardwww [97]
2 years ago
8

THE SUM 10 INFINITY OF A GEOMETRIC SERIES IS 100. FIND THE TERM IF THE COMMON FIRST RATIO IS - 1/2​

Mathematics
1 answer:
zhuklara [117]2 years ago
6 0

Answer:

a = 150

Step-by-step explanation:

<u>Sum to infinity of a geometric series</u>

S_{\infty}=\dfrac{a}{1-r}\:\textsf{ for }|r| < 1

where:

  • a is the first term
  • r is the common ratio

Given:

  • S_{\infty}=100
  • r=-\dfrac{1}{2}

Substitute the given values into the formula and solve for a:

\begin{aligned}S_{\infty} & =\dfrac{a}{1-r}\\\\\implies 100 & =\dfrac{a}{1-\left(-\frac{1}{2}\right)}\\\\ 100 & =\dfrac{a}{1+\frac{1}{2}}\\\\100 & = \dfrac{a}{\frac{3}{2}}\\\\a & = \dfrac{3}{2} \cdot 100\\\\a & = 150\end{aligned}

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Find the HCF of 12 and 28​
Vitek1552 [10]

Answer:4

Step-by-step explanation:The GCF of 12 and 28 is 4. To calculate the GCF (Greatest Common Factor) of 12 and 28, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 12 and 28

8 0
2 years ago
Aaron claims the same answer could also be found by adding either –5 + 3 or –3 + 5.
Debora [2.8K]

Answer:

Step-by-step explanation:

-5 + 3 = -2  -5 is larger

5 + (-3) = 2   5 is larger

2 is larger than -2

8 0
3 years ago
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A person is training for a cross country and manages to run 2 miles in a time of 12 mins what was the runners average velocity i
spin [16.1K]

Answer:

10 miles per hour

Step-by-step explanation:

Average velocity=distance covered/time in hours

Distance=2 miles

time=12minute

change minutes to hour=12/60 =0.2hrs

v=2÷0.2

v=10miles per hour

5 0
3 years ago
Read 2 more answers
Which of the following is the balance for a single $2700 deposit in an account with an APR of 4.5% that compounds interest month
Zanzabum

The future amount is $3697.52, if a a single $2700 deposit in an account with an APR of 4.5% that compounds interest monthly and is invested for 7 years.

Step-by-step explanation:

The given is,

                     A single deposit amount - $ 2700

                                                       APR - 4.5%

                                            ( Compounded monthly )

                                                    Period - 7 years

Step:1

                 Formula to find future amount with an APR compounded monthly,

                                                          A = P(1+\frac{r}{n})^{nt}.......................(1)

                Where, A - Future amount

                             P - Initial deposit

                              r - Interest rate

                             n - Number of compounding in a year

                             t - No.of years

                From given,

                         P = $ 2700

                          r = 4.5%

                          n = 12                   (∵ For monthly n becomes 12 )

                           t = 7 years

                   Equation (1) becomes,

                                                           = 2700(1+\frac{0.045}{12})^{(12)(7)}

                                                           = 2700(1+0.00375)^{84}

                                                           = 2700(1.36945)

                                                           = 3697.52

                                                       A = $3697.52

Result:

              The future amount is $3697.52, if a a single $2700 deposit in an account with an APR of 4.5% that compounds interest monthly and is invested for 7 years.

3 0
4 years ago
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sertanlavr [38]
4-4=0
-4+3=-1
-2-5= -7
b) [0 -1 -7]<span />
4 0
3 years ago
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