Chapter MPS, Problem 11.3MPS

a.

To determine

Equation for $n$ number of beads in $nth$ row.

Answer to Problem 11.3MPS

  $a_n=15n-5$ is equation for $n$ number of beads in $nth$ row.

Explanation of Solution

Given information:

Alberta is creating beadwork in which starting row has 10 coloured beads, and the consecutive row are having 15 more beads than the previous one.

Formula used:

Nth term of arithmetic sequence:

  $a_n=a+\left(n-1\right)d$

  a = First term of the series.

  d = Common difference

  n= Number of terms

  $a_n$ = nth term

As we know the first row has 10 beads, therefore $a=10$

And the difference between two consecutive rows is 15, therefore $d=15$

Now finding beads in nth row using formula $a_n=a+\left(n-1\right)d$

Here $a=10,d=15$

  $\begin{array}{l}{a}_n=10+\left(n-1\right)15\\ a_n=10+15n-15\\ \boxed{a_n=15n-5}\end{array}$

  $a_n=15n-5$ is equation for $n$ number of beads in $nth$ row.