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sergey [27]
4 years ago
15

The formula to find a certain number in an arithmetic sequence is an=a1+d(n−1)an=a1+d(n−1) .

Mathematics
2 answers:
noname [10]4 years ago
5 0

Answer: n=\dfrac{a_n-a_1}{d}+1

Step-by-step explanation:

Given : The formula to find a certain number in an arithmetic sequence is

a_n=a_1+d(n-1), where a_n is the nth term , a_1 is the first term and d is the common difference.

To solve the formula for n , first subtract a_1 from both sides , we get

a_n-a_1=d(n-1)

Now, divide d on both sides , we get

\dfrac{a_n-a_1}{d}=n-1

Now, add 1 to the both sides , we get

\dfrac{a_n-a_1}{d}+1=n

Or

n=\dfrac{a_n-a_1}{d}+1

cluponka [151]4 years ago
4 0
The formula of arithmetic sequence is
an = a₁ + d(n - 1)

Then we need to find the formula to determine n. I reverse the equation so the 'n' will be on the left side.
a₁ + d(n - 1) = an

Then I move all the terms on the left one by one to the right side except n
a₁ + d(n - 1) = an
d(n - 1) = an - a₁
n - 1 = (an - a₁)/d
n = 1 + (an - a₁)/d

This is the formula to solve n
n = 1 + (an - a₁)/d
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lidiya [134]

Answer:

56.25 pound of the coffee that costs $5 per pound is needed

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Step-by-step explanation:

Let the number of pounds be x and y respectively

The total pounds is 75;

So;

x + y. = 75 •••••••(i)

Total cost of first type

9 * x = $9x

Total cost of second type;

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6 * 75 = $450

Thus;

9x + 5y = 450 ••••••••(ii)

From i, x = 75-y

Put this into ii

9(75-y) + 5y = 450

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4y = 675-450

4y = 225

y = 225/4

y = 56.25

x = 75 - y from i

x = 75-56.25

x = $18.75

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