Question

Find the 50th term of this arithmetic sequence: 6, 13, 20, 27, .

Answer 1

$\bf 6~~,~~\stackrel{6+7}{13}~~,~~\stackrel{13+7}{20}~~,~~\stackrel{20+7}{27}~\hspace{10em} d=7 \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ d=7\\ a_1=6\\ n=50 \end{cases} \\\\\\ a_{50}=6+(50-1)7\implies a_{50}=6+(49)7\implies a_{50}=6+343\implies a_{50}=349$

Answer 2

To find a specific term in an arithmetic sequence, we can use this formula: a(n) = a(1) + d(n - 1)

Plug in the appropriate values.

a(n) = final term

a(1) = first term

d = difference

n = term

a(50) = 6 + 7(50 - 1)

a(50) = 349

The value of the 50th term in the sequence is 349.