8 and 11
Given the sequence of numbers -1, 2, 5 __, __, you are to find the next two terms of the sequence.
The sequence is an arithmetic sequence and the nth term of an arithmetic sequence is expressed as:
[tex]T_n=a+(n-1)d[/tex]where:
• a is the, first term
,• n is the, number of terms
,• d is the ,common difference
From the given sequence;
a = -1
d = 2 - (-1) = 5 - 2
d = 3
For the fourth term, n = 4.
[tex]\begin{gathered} T_4=-1+(4-1)\cdot3 \\ T_4=-1+3(3) \\ T_4=-1+9 \\ T_4=8 \end{gathered}[/tex]For the fifth term, n = 5;
[tex]\begin{gathered} T_5=-1+(5-1)\cdot3 \\ T_5=-1+4(3) \\ T_5=-1+12 \\ T_5=11 \end{gathered}[/tex]Therefore the next two terms of the given arithmetic sequence are 8 and 11