# Find the term n=12, given the arithmetic sequence a_1=5 and d=1/3

Find the term n=12, given the arithmetic sequence ${a}_{1}=5$ and d=1/3
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

wespee0
The ${n}^{\text{th}}$ term, ${a}_{n}$ of an arithmetic sequence, with initial term, ${a}_{1}$ and incremental difference d is given by the formula:
$\text{XXX}{a}_{n}={a}_{1}+\left(n-1\right)\cdot d$
In this case with $n=12,{a}_{1}=5,\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}d=\frac{1}{3}$
$\text{XXX}{a}_{12}=5+\left(12-1\right)\cdot \frac{1}{3}=5+\frac{11}{3}=8\frac{2}{3}$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 37, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}