Question

A marching band is arranged in rows of 7 the first row has 3 band members and each row after the first has 2 more band members than the row before it write a rule for the number of band members in the nth row. Then find the total number of band members.

Answer 1

Answer:

$a_{n}$= 1+2n and 63

Step-by-step explanation:

the question belongs to arithmetic sequence and $a_{n}$ can be determined by the formula

$a_{n}$= a1 + d (n-1)

Let " $a_{n}$ " 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:

$a_{n}$= 3 + 2(n-1)

$a_{n}$= 3 + 2n -2

$a_{n}$= 1+2n

-> In order to find total number of band members '$S_{7}$'

Let $S_{n}$ represent total number in n rows

We'll use the formula, i.e  $S_{n}$ = n/1 ($a_{1}$ +  $a_{n}$)

where, n is the number of terms, $a_{1}$ is the first term and $a_{n}$ is the last term

So,

n=7

$a_{7}$ = 1 + 2(7)= 15

=>$S_{7}$ = 7/2 (3 + 15)

$S_{7}$ = 63

The total number of band members are 63