A term in an arithmetic sequence and the common difference. Given a_15=272 and d=20, how do you find the first three terms?

Dec 21, 2016

$- 8 , 12 , 32$

Explanation:

For the standard arithmetic sequence, the nth term is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{a}_{n} = {a}_{1} + \left(n - 1\right) d} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ${a}_{1} \text{ is first term}$

here ${a}_{15} = 272 \text{ and } d = 20$

and we want to find ${a}_{1} , {a}_{2} \text{ and } {a}_{3}$

$\Rightarrow 272 = {a}_{1} + \left(14 \times 20\right)$

$\Rightarrow {a}_{1} = 272 - 280 = - 8$

$\Rightarrow {a}_{2} = - 8 + d = - 8 + 20 = 12$

$\Rightarrow {a}_{3} = 12 + 20 = 32$