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3 years ago

What is the eighth term in the arithmetic sequence defined by the explicit formula an=5n+3 ?

Mathematics

1 answer:

beks73 [17]3 years ago

3 0

The eighth term of the arithmetic sequence is 43

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

$a_{n}=a+(n-1)d$ , where

a is the 1st term
d is the common difference between the consecutive terms
n is the position of the term

∵ The explicit formula of an arithmetic sequence is $a_{n}=5n + 3$ ,

where n is the position of the term

∵ We need to find the eighth term

- That means the position of the term is 8th in the sequence

∴ n = 8

- Substitute n by 8 in the given formula

∴ $a_{8}=5(8)+3$

∴ $a_{8}=40+3$

∴ $a_{8}=43$

The eighth term of the arithmetic sequence is 43

Learn more:

You can learn more about the arithmetic sequences in brainly.com/question/7221312

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Let sugar be the explanatory variable and calories be the response variable; which scenario best describes ŷ = 57 + 2.5x?

algol13

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The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.

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Explanation:

x = amount of sugar (in grams)

y = number of calories in the juice

ŷ = estimate of y, so its the estimate of calories in the juice

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This is in the form y = mx+b where m = 2.5 is the slope and b = 57 is the y intercept.

The slope tells us what the rate of change is. Specifically, it tells us how much the amount of calories (y) is going up each time the amount of sugar (x) goes up. Each time x goes up by 1, y goes up by 2.5

The y intercept 57 is the starting or initial amount of calories. If you have 0 grams of sugar, the lowest amount of sugar possible, then you start off with 57 calories. We can see this by plugging x = 0 into ŷ = 2.5x + 57 (you should get ŷ = 57). Visually, the y intercept is where the line crosses the y axis.

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