Answer:
[tex]a_{n}[/tex]= 1+2n and 63
Step-by-step explanation:
the question belongs to arithmetic sequence and [tex]a_{n}[/tex] can be determined by the formula
[tex]a_{n}[/tex]= a1 + d (n-1)
Let " [tex]a_{n}[/tex] " represents the number of band members in the nth row
and 'd' represents the common difference.( as stated each row has 2 more band members than the row before it)
therefore, d=2
'a1' represents first row that has three members. So, a1 = 3
->Rule for nth term will be:
[tex]a_{n}[/tex]= 3 + 2(n-1)
[tex]a_{n}[/tex]= 3 + 2n -2
[tex]a_{n}[/tex]= 1+2n
-> In order to find total number of band members '[tex]S_{7}[/tex]'
Let [tex]S_{n}[/tex] represent total number in n rows
We'll use the formula, i.e [tex]S_{n}[/tex] = n/1 ([tex]a_{1}[/tex] + [tex]a_{n}[/tex])
where, n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term
So,
n=7
[tex]a_{7}[/tex] = 1 + 2(7)= 15
=>[tex]S_{7}[/tex] = 7/2 (3 + 15)
[tex]S_{7}[/tex] = 63
The total number of band members are 63
