How do you write the first five terms of the arithmetic sequence given a_1=5, d=-3/4?

Jun 14, 2017

The equation for the nth term is:

${a}_{n} = {a}_{1} + d \left(n - 1\right)$

Explanation:

Substituting in the given values:

${a}_{n} = 5 - \frac{3}{4} \left(n - 1\right)$

${a}_{1} = 5 - \frac{3}{4} \left(1 - 1\right) = 5$

${a}_{2} = 5 - \frac{3}{4} \left(2 - 1\right) = \frac{17}{4}$

${a}_{3} = 5 - \frac{3}{4} \left(3 - 1\right) = \frac{14}{4}$

${a}_{4} = 5 - \frac{3}{4} \left(4 - 1\right) = \frac{11}{4}$

${a}_{5} = 5 - \frac{3}{4} \left(5 - 1\right) = 2$