Answer:
191
Step-by-step explanation:
First, determine if the sequence is arithmetic or geometric.
If it is arithmetic, the difference between consecutive terms is constant.
If it is geometric, the ratio between consecutive terms is constant.
[tex]\sf 11 \underset{+4}{\longrightarrow} 15 \underset{+4}{\longrightarrow} 19[/tex]
As we add 4 to each term to get the next term, this is an arithmetic sequence with common difference of 4.
Arithmetic sequence
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
- [tex]a_n[/tex] is the nth term
- a is the first term
- d is the common difference between terms
Given:
Substituting the given values into the formula to find an equation for the nth term:
[tex]\implies a_n=11+(n-1)4[/tex]
[tex]\implies a_n=4n+7[/tex]
Therefore, to find the 46th term, substitute n = 46 into the equation:
[tex]\implies a_{46}=4(46)+7=191[/tex]
