Question

The first three terms of an arithmetic sequence are as follows.-26, -19, -12Find the next two terms of this sequence.-26, – 19, -12,

Answer 1

`The\:next\:terms\:are:-5,\:and\:2`

1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:

`\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ d=7 \end{gathered}`

2) Based on that, we can do the following to find the next two terms:

`\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ -12+7=-5 \\ -5+7=2 \\ \\ -19,-12,-5,2 \\ Or \\ \\ a_4=a_1+d(n-1) \\ a_4=-26+7(4-1) \\ a_4=-26+21 \\ a_4=-5 \\ \\ a_5=-26+7(5-1) \\ a_5=-26+7(4) \\ a_5=-26+28 \\ a_5=2 \end{gathered}`

Thus, the next terms are -5 and 2