Question

Write an equation for the n term of the arithmetic sequence -1, 4, 9, 14, . Then find a50

Answer 1

Step-by-step explanation:

The sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = - 1

To find the common difference subtract the previous term from the next term

We have

d = 4 --1 = 4 + 1 = 5 or 9 - 4 = 5

Therefore d = 5

Substitute the values into the general formula

That's

$A(n) = - 1 + (n - 1)(5) \\ = - 1 + 5n - 5 \\ = 5n - 6 \: \: \: \: \: \: \: \: \: \: \:$

To find A(50) substitute the value of n that's 50 into the formula above

$A(50) = 5(50) - 6 \\ \: \: \: \: \: \: \: \: \: = 250 - 6 \\ \: = 244$

Hope this helps you

Answer 2

Step-by-step explanation:

The sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

• A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

• a = - 1

To find the common difference subtract the previous term from the next term

• d = 4 --1 = 4 + 1 = 5 or 9 - 4 = 5

Therefore d = 5

Substitute the values into the general formula

That's

$A(n)=−1+(n−1)(5) \\ \: \: \: \: \: \: \: \: =−1+5n−5 \\ =5n−6$

To find A(50) substitute the value of n that's 50 into the formula above

$A(50)=5(50)−6 \\ \: \: \: \: \: \: \: \: =250−6 \\ \: \: =244$