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stiks02 [169]
3 years ago
13

the fourth term of an arithmetic sequence is 141, and the seventh term is 132. what is the first term?

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
7 0
The 1st, 4th, and 7th terms make an arithmetic sequence of their own. The 4th term is the average of the 1st and 7th, so ...
   (1st +7th)/2 = 4th
   1st + 7th = 2×4th
   1st = 2×4th - 7th

The first term is ...
   2*141 - 132 = 150
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Option A

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<u>Solution:</u>

Given, equation is -2(x-2)^{2}+5=0

We have to solve for the x and choose from the options given,

Now, take the equation,

\begin{array}{l}{\rightarrow-2(x-2)^{2}+5=0} \\\\ {\rightarrow-2(x-2)^{2}=-5}\end{array}

Negative sign cancels on both sides

\begin{array}{l}{\rightarrow 2(x-2)^{2}=5} \\\\ {\rightarrow(x-2)^{2}=\frac{5}{2}}\end{array}

Taking square root on both sides, we get

\begin{array}{l}{\rightarrow x-2=\sqrt{\frac{5}{2}}} \\\\ {\rightarrow x-2=\pm 1.58} \\\\ {\rightarrow x=2 \pm 1.58}\end{array}

\begin{array}{l}{\rightarrow x=2+1.58 \text { or } 2-1.58} \\\\ {\rightarrow x=3.58 \text { or } 0.42}\end{array}

Hence, the values of x are 3.58 or 0.42, so option A is correct.

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2 years ago
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Kiran's mother gets a restaurant bill for $25. She has a coupon for 15% off. After the
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Answer:

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Step-by-step explanation:

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Our total is now $21.25

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3 years ago
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Answer:

We conclude that the total amount accrued, principal plus interest,  from compound interest on an original principal of  $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

Interest rate r = 5% = 0.05

Time period t = 8 years

To determine

Accrue Amount A = ?

Using the compound interest equation

A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

where:

A represents the Accrue Amount

P represents the Principal Amount

r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

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now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}

\:A=2500\left(1+\frac{0.05}{6}\right)^{48}

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A=\:3723.38 $

Therefore, we conclude that the total amount accrued, principal plus interest,  from compound interest on an original principal of  $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

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Answer:

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