Notice that the given sequence has a common difference of 7. Then, the sequence is an arithmetic sequence with first term -11 and common difference of 7.
The recursive formula for a sequence with those characteristics, is:
[tex]\begin{gathered} a_n=a_{n-1}+7 \\ a_1=-11 \end{gathered}[/tex]The explicit formula for a sequence with those characteristics, is:
[tex]\begin{gathered} a_n=-11+7(n-1) \\ =-11+7n-7 \\ =7n-18 \end{gathered}[/tex]Use the explicit formula to find the 10th term, the 15th term and the 30th term:
[tex]\begin{gathered} a_{10}=-11+7(10-1) \\ =-11+7\cdot9 \\ =-11+63 \\ =52 \end{gathered}[/tex][tex]\begin{gathered} a_{15}=-11+7(15-1) \\ =-11+7\cdot14 \\ =-11+98 \\ =87 \end{gathered}[/tex][tex]\begin{gathered} a_{30}=-11+7(30-1) \\ =-11+7\cdot29 \\ =-11+203 \\ =192 \end{gathered}[/tex]Check each statement to see if they are correct or not:
A: True
B: False
C: True
D: False
E: True
