Question

What is the nineteenth term of an arithmetic sequence with first term 9 and common difference 5?

Answer 1

Answer:

The 19th term is 99.

Step-by-step explanation:

We can write a direct formula and use it to find the 19th term. Recall that the direct formula for an arithmetic sequence is given by:

$x_n = a + d(n-1)$

Where a is the initial term and d is the common difference.

Since the first term is 9 and the common difference is 5:

$\displaystyle x _ n = 9+5(n-1)$

To find the 19th term, let n = 19. Thus:

$x_{19} = 9+5(19-1)$

And evaluate:

$\displaystyle \begin{aligned} x_{19} &= 9+5(18) \\ &= 9+90 \\ &= 99\end{aligned}$

The 19th term is 99.