How do you write a rule for the nth term of the arithmetic sequence and then find a_10 for 1/4, 0, -1/4, -1/2, -3/4?

Feb 3, 2018

${a}_{10} = 2$

Explanation:

Given the Arithmetic sequence
${a}_{1} = \left(\frac{1}{4}\right) , {a}_{2} = 0 , {a}_{3} = - \frac{1}{4} , \ldots$

common difference $d = {a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = a 4 - {a}_{3}$ for A. P.

$d = 0 - \frac{1}{4} = - \frac{1}{4}$

${n}^{t h}$ Term ${a}_{n} = a + \left(\left(n - 1\right) \cdot d\right)$

${10}^{t h} T e r m$ ${a}_{10} = a + \left(\left(10 - 1\right) \cdot d\right)$

=> (1/4) + ( 10-1) * (-1/4)) = 1/4 - (9 * (1/4))

$\implies \frac{1}{4} - \frac{9}{4} = \frac{8}{4} = 2$