Question

Write an equation for the nth term of the arithmetic sequence: 15,28,41 ....

Answer 1

Answer:

The equation for the nth term of  the given arithmetic sequence is: $\mathbf{a_n=13n+22}$

Step-by-step explanation:

We need to write an equation for the nth term of  the arithmetic sequence:

15,28,41 ....

The equation for arithmetic sequence is: $a_n=a_1+(n-1)d$

Where $a_n$ is the nth term, $a_1$ is first term and d is common difference

In the given sequence we have:

a₁ = 15

a₂ = 28

We can find common difference using the formula:

$a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13$

So, the common difference d is 13

Now, equation for nth term will be:

$a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2$

So, the equation for the nth term of  the given arithmetic sequence is: $\mathbf{a_n=13n+22}$

where n=1,2,3..