Question

Write the first five terms of the sequence defined by the recursive formula a,= 2 ((n-1)+3, with a =-2.O A -2,-1,1,5,13O B. -2,1,4,7,10OC -2,2,10,26,58OD. -2,-4.-10.-28.-82V2

Answer 1

given data;

$\begin{gathered} a_n=2(a_{n-1})+3 \\ a_1=-2 \end{gathered}$

to find the first five terms

$\begin{gathered} a_2=2(a_{2-1})+3 \\ =2a_1+3 \\ =2(-2)+3 \\ =-4+3 \\ a_2=-1 \end{gathered}$$\begin{gathered} a_3=2a_2+3 \\ =2(-1)+3 \\ =-2+3 \\ =1 \end{gathered}$$\begin{gathered} a_4=2a_3+3 \\ =2\cdot1+3 \\ =2+3 \\ a_4=5 \end{gathered}$$\begin{gathered} a_5=2a_4+3 \\ =2\cdot5+3 \\ =10+3 \\ =13 \end{gathered}$

thus, the first five terms are,

$-2,-1,1,5,13$

thus the answer is, option A) -2,-1,1,5,13.