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

User Paridokht
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Answer:

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.

User Daniel Corona
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