Question

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

Answer 1

The 19th term is 99.

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.