Write an equation for the nth term of the arithmetic sequence -13,-8,-3,2........
a = -13 , d = 5
term(n) = a + (n-1)d
= -13 + 5(n-1)
= -13 + 5n - 5
= 5n - 18
To find the equation for the nth term of an arithmetic sequence, we first need to determine the common difference. In this sequence, we can see that the common difference is 5 because each term increases by 5.
Now, let's find the equation for the nth term using the formula for arithmetic sequences:
nth term = first term + (n - 1) * common difference
In this case, the first term is -13 and the common difference is 5. Plugging these values into the formula, we get:
nth term = -13 + (n - 1) * 5
Therefore, the equation for the nth term of the sequence -13, -8, -3, 2... is:
nth term = -13 + 5n - 5
nth term = 5n - 18
To find the nth term of an arithmetic sequence, we first need to identify the common difference (d) between consecutive terms. In this case, we can see that the common difference is 5 because each term is obtained by adding 5 to the previous term.
Now let's use this information to derive the equation for the nth term. We can start by determining the first term (a₁) of the sequence, which is -13.
The formula for finding the nth term of an arithmetic sequence is:
nth term (an) = a₁ + (n - 1) * d
Plugging in the values we have:
nth term (an) = -13 + (n - 1) * 5
Therefore, the equation for the nth term of the given arithmetic sequence is:
an = -13 + 5n - 5
Simplifying further:
an = 5n - 18