Question

an arithmetic sequence has these properties: a1=2an = an-1 + 5 what are the first four terms of the sequence?

Answer 1

we have that the arithmetic sequence have:

$\begin{gathered} a_1=2 \\ a_n=a_{n-1}+5 \end{gathered}$

so we can replace for n=2,3,and 4 to find the first four terms so:

for n=2

$\begin{gathered} a_2=a_{2-1}+5 \\ a_2=a_1+5 \\ a_2=2+5 \\ a_2=7 \end{gathered}$

for n=3

$\begin{gathered} a_3=a_{3-1}+5 \\ a_3=a_2+5 \\ a_3=7+5 \\ a_3=12 \end{gathered}$

and for n=4

$\begin{gathered} a_4=a_{4-1}+5 \\ a_4=a_3+5 \\ a_4=12+5 \\ a_4=17 \end{gathered}$

So the first four numbers are

$2,7,12,17$