Find the tenth term in each sequence. -1,2/3,7/3,4,17/3

Mathematics

1 answer:

Luba_88 [7]2 years ago

5 0

It'a an arithmetic sequence:

$a_1=-1\\\\a_2=-1+\dfrac{5}{3}=-\dfrac{3}{3}+\dfrac{5}{3}=\dfrac{2}{3}\\\\a_3=\dfrac{2}{3}+\dfrac{5}{3}=\dfrac{7}{3}\\\\a_4=\dfrac{7}{3}+\dfrac{5}{3}=\dfrac{12}{3}=4\\\\a_5=4+\dfrac{5}{3}=\dfrac{12}{3}+\dfrac{5}{3}=\dfrac{17}{3}\\\vdots\\\\\text{The general formula for nth term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\\\\\text{We have}\ a_1=-1\ \text{and}\ d=\dfrac{5}{3}.\\\\\text{Substitute}\\\\a_n=-1+(n-1)\left(\dfrac{5}{3}\right)=-1+\dfrac{5}{3}n-\dfrac{5}{3}=\dfrac{5}{3}n-\dfrac{3}{3}-\dfrac{5}{3}$

$\boxed{a_n=\dfrac{5}{3}n-\dfrac{8}{3}}$

You might be interested in

Latrell bought 4 bags of powdered sugar. He got a total of 5 1/2 cups of sugar. How many cups of sugar were in each bag?

Stels [109]

So all 4 bags of sugar yielded 5 and 1/2 cups..... well.. how many in each one? well, let's split the 5 and 1/2 evenly in 4 pieces.

$\bf \stackrel{mixed}{5}\frac{1}{2}\implies \cfrac{5\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{11}{2}}\\\\
-------------------------------\\\\
\cfrac{\quad\frac{11}{2} \quad }{4}\implies \cfrac{\quad\frac{11}{2} \quad }{\frac{4}{1}}\implies \cfrac{11}{2}\cdot \cfrac{1}{4}\implies \cfrac{11}{8}\implies \stackrel{cups}{1\frac{3}{8}
}$

5 0

3 years ago

Rayshawn has a certain amount of money if he spends $20 then he has 1/3 of the original amount how much money did Rayshawn have

erik [133]

Answer:

Rayshawn originally had $30.

Step-by-step explanation:

i) Rayshawn has a certain amount of money. Let us say this amount is $x.

ii) Rayshawn spends $20 which means that he is left with $(x - 20)

iii) it is also given that amount of money left after spending $20 is $\dfrac{1}{3}$ of the original amount, $x, the amount remaining is $\dfrac{\$x}{3}$ .

iv) from the information given in ii) and iii) we get

$(x - 20) = $\dfrac{\$x}{3}$ , Therefore we get 3x - 60 = x , therefore 2x = 60,

Therefore x = $30. Rayshawn originally had $30.

7 0

3 years ago

Which sequence is modeled by the graph below? coordinate plane showing the points 1, 4; 2, 0.8; and 3, 0.16

Olin [163]

2nd one: an = 4(1/5)^n - 1

8 0

3 years ago

Read 2 more answers

A juggler tosses a bowling pin in the air with an initial velocity of 18 ft per second. It leaves his hand when it is five feet

Natali5045456 [20]

Complete Question

A juggler tosses a bowling pin in the air with an initial velocity of 18 ft per second. It leaves his hand when it is five feet from the ground and he catches it when it is four feet from the ground,How long is the ball in the air?

Answer:

$t\approx 0.1s$