Question

David saved $5 in the first week of a year and then increased his weekly savings by $1.75. If in the nth week, his weekly savings become $20.75, find the value of 'n'.

• A. 18
• B. 13
• C. 10
• D. 5

Answer 1

The correct option is C 10

David saved $5 in the first week and then started increasing his savings each week by $1.75.

So, David's weekly savings form an arithmatic progression.

Hence,

First term, a = 5
Common difference, d = 1.75

Also given,
a_n = 20.75

As we know, by the nth term formula,
a_n = a + (n − 1) d

Therefore, we get:
$20.75=5+(n-1)\times 1.75$

$\Rightarrow 15.75=(n-1)\times 1.75$

$\Rightarrow (n–1)=\frac{15.75}{1.75}=\frac{1575}{175}=\frac{63}{7}=9$

$\Rightarrow (n–1)=9$
$\Rightarrow n=10$

Hence, the value of 'n' is 10.