Answer:
[tex]\bold{n =2t-1}[/tex]
Step-by-step explanation:
Given table is:
[tex]\begin{center}\begin{tabular}{ c c}Term Number (t) & Number of triangles (n) \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\\end{tabular}\end{center}[/tex]
i.e. when term number, t = 1, number of triangles (n) = 1
when term number, t = 2, number of triangles (n) = 3
when term number, t = 3, number of triangles (n) = 5
when term number, t = 4, number of triangles (n) = 7
If we closely look at the pattern, number of triangles (n) in each row are 1 lesser than twice of term number (t).
i.e. for [tex]t=1, n = 2\times 1 -1=1[/tex]
[tex]t=2, n = 2\times 2 -1=3[/tex]
[tex]t=3, n = 2\times 3 -1=5[/tex]
[tex]t=4, n = 2\times 4 -1=7[/tex]
Therefore, the number of triangles in the nth term will be given as:
[tex]\bold{n =2t-1}[/tex]
