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weqwewe [10]
3 years ago
15

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

Mathematics
1 answer:
Doss [256]3 years ago
7 0

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 <em>a</em> is the initial term and <em>d</em> 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 <em>n</em> = 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.

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