In a line of students, Jenna is number 8.The teacher says that a rule for a number pattern is add 4. The first student inline says the first term, 7. What number should Jenna say?
Answer:
Formula for nth term in Arithmetic sequences is:
\(a_n =a+(n-1)d\)
where a is the first term, d is the common difference and n is the number of terms.
As per the statement:
The rule for the pattern is add 4.
As the first term in line says the first term i,e 7
\(a= 7\)
common difference(d)= 7
As the Jenna number is 8th in line.
Series we get;
7, 11, .........\(a_8\)
We have to find the 8th term.
n = 8, a = 7 and d = 4
Using above formula:
\(a_8 = 7+(8-1)4 = 7+7 \cdot 4 = 7 +28 = 35\)
Therefore, 35 number should Jenna say.