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3 years ago

What is the third term of an arithmetic sequence whose second term is 7 and whose sixth term is 23

Mathematics

1 answer:

ohaa [14]3 years ago

3 0

Answer: 11

Step-by-step explanation:

Given

The second term of an AP is 7

The sixth term of an AP is 23

Suppose a and d be the first term and common difference of the sequence

$\Rightarrow 7=a+d\quad \ldots(i)\\\Rightarrow 23=a+5d\quad \ldots(ii)$

Subtract the above equations

$\Rightarrow 23-7=5d-d\\\Rightarrow 16=4d\\\Rightarrow d=4$

Put d in equation (i)

$\Rightarrow 7=a+4\\\Rightarrow a=3$

So, the third term of the AP is $a+2d$

$\Rightarrow 3+2\times 4=11$

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−4 4/5 ÷ 4 A. -1 1/5 B. -4/5 C. 4/5 D. 1 1/5

kogti [31]

Answer:

A. -1⅕

Step-by-step explanation:

$-4\frac{4}{5}\div 4 = -4,8\div 4 = -1,2 = -1 \frac{1}{5}$

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7 0

3 years ago

Kristen invests $ 5745 in a bank. The bank 6.5% interest compounded monthly. How long must she leave the money in the bank for i

podryga [215]

Answer:

1. 10.7 years

2. 17.0 years

3. 2nd option

Step-by-step explanation:

Use formula for compounded interest

$A=P\cdot \left(1+\dfrac{r}{n}\right)^{nt},$

where

A is final value, P is initial value, r is interest rate (as decimal), n is number of periods and t is number of years.

In your case,

1. P=$5745, A=2P=$11490, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$11490=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},\\ \\2=(1.0054)^{12t},\\ \\12t=\log_{1.0054}2,\\ \\t=\dfrac{1}{12}\log_ {1.0054}2\approx 10.7\ years.$

2. P=$5745, A=3P=$17235, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$17235=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},$

$3=(1.0054)^{12t},$

$12t=\log_{1.0054}3,$

$t=\dfrac{1}{12}\log_{1.0054}3\approx 17.0\ years.$

3. 1 choice: P=$5745, n=12 (compounded monthly), r=0.065 (6.5%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12\cdot 5},\\ \\A=5745\cdot (1.0054)^{60}\approx \$7936.39.$

2 choice: P=$5745, n=4 (compounded monthly), r=0.0675 (6.75%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.0675}{4}\right)^{4\cdot 5},\\ \\A=5745\cdot (1.0169)^{20}\approx \$8032.58.$

The best will be 2nd option, because $8032.58>$7936.39

5 0

3 years ago

Read 2 more answers

Susie has 4 gallons of juice.How many cups of juice does she have? ANSWER QUICKLY

IgorLugansk [536]

Answer: 64 cups

Step-by-step explanation:

Each gallon has 16 cups so you multiply 16 by 4 because there are 4 gallons and you get 64. Hope that helped. :)

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3 years ago

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Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5. Ann paid a total o

adell [148]

Answer:

$2.10x + 5= $49.10

x=21

Step-by-step explanation:

the x is used for a variable that changes and in this case the mph changes which lead x being the amount of miles that they had drove which at the end ends up multi. with the $2.10 . as for the 5 it was an initial as in it doesn't change.

for the second part

you subtract 5 from each side so you have the total of 2.10x= 44.10 then u divide 2.10 from each side and that will give you x = 21

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3 years ago

Look at the picture please help

morpeh [17]

Answer:

Step-by-step explanation:

First off, we know that (g ° f)(2) is just both functions done in a ordered fashion. In this case, f(x) is done first.

To figure out what f(2) is, all we have to do is find where x = 2 is on the graph. In this case it is on point (2, 3). The input is the x and the output is the y, so f(2) = 3.

Then, we can figure out what g(3) by locating x = 3 on line g. It shows the point (3, 0). This means that g(3) = 0.

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2 years ago

What is the third term of an arithmetic sequence whose second term is 7 and whose sixth term is 23​

What is the third term of an arithmetic sequence whose second term is 7 and whose sixth term is 23