Question

FIND THE FIRST 5 TERMS OF THIS SEQUENCE:a1 = -4, a(n+1) = an + n^2

Answer 1

Okay, here we have this:

Considering the provided information, we are going to find the first 5 terms of the sequence, so we obtain the following:

$\begin{gathered} a_1=-4 \\ a_{n+1}=a_n+n^2 \end{gathered}$

Then, replacing n we have:

$\begin{gathered} a_{1+1}=a_1+1^2 \\ a_2=-4+1 \\ a_2=-3 \end{gathered}$

$\begin{gathered} a_{2+1}=a_2+2^2 \\ a_3=-3+4 \\ a_3=1 \end{gathered}$

$\begin{gathered} a_{3+1}=a_3+3^2 \\ a_4=1+9 \\ a_4=10 \end{gathered}$

$\begin{gathered} a_{4+1}=a_4+4^2 \\ a_5=10+16 \\ a_5=26 \end{gathered}$

Finally we obtain that the first 5 terms of this sequence are -4, -3, 1, 10 and 26.