# How do you find the first five terms of the arithmetic sequence given a_1=6 and d=-4?

Nov 15, 2016

First five terms are $\left\{6 , 2 , - 2 , - 6 , - 10\right\}$

#### Explanation:

In an arithmetic sequence, starting from first term as ${a}_{1}$ and common difference $d$, successive terms are obtained by adding $d$ i.e. ${a}_{2} = {a}_{1} + d$, ${a}_{3} = {a}_{2} + d$, ........ ,${a}_{n} = {a}_{n - 1} + d$

Hence as ${a}_{1} = 6$ and $d = - 4$

${a}_{2} = {a}_{1} + d = 6 + \left(- 4\right) = 6 - 4 = 2$

${a}_{3} = {a}_{2} + d = 2 + \left(- 4\right) = 2 - 4 = - 2$

${a}_{4} = {a}_{3} + d = - 2 + \left(- 4\right) = - 2 - 4 = - 6$

${a}_{5} = {a}_{4} + d = - 6 + \left(- 4\right) = - 6 - 4 = - 10$

Hence, first five terms are $\left\{6 , 2. - 2 , - 6 , - 10\right\}$