We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
224
2
avatar+1110 

 

It took Lara five days to read a novel. Each day after the first day, Lara read half as many pages as the day before. If the novel was 248 pages long, how many pages did she read on the first day?

 Sep 3, 2018
 #1
avatar
0

n + (1/2)n +(1/4)n + (1/8)n +(1/16)n=248, solve for n

 

n=128 pages Lara read on first day. So that you have:

128, 64, 32, 16, 8 =248

 Sep 3, 2018
 #2
avatar+22172 
+3

It took Lara five days to read a novel. Each day after the first day,
Lara read half as many pages as the day before.
If the novel was 248 pages long,
how many pages did she read on the first day?

 

Sequence is a geometric sequence:

 

Formula:
\(a_n = a\cdot r^{n-1} \\ sum~ s_n = \dfrac{a\left(1-r^{n+1}\right)} {1-r} \)

 

\(\begin{array}{|rcll|} \hline s_n &=& \dfrac{a\left(1-r^{n}\right)} {1-r} \quad & | \quad n=5,~ r=\dfrac12,~ s_n = 248 \\\\ 248 &=& \dfrac{a\left(1-\left(\dfrac12 \right)^{5}\right)} {1-\dfrac12} \\\\ 248 &=& \dfrac{a\left(1-\dfrac{1}{2^5}\right)} {\dfrac12} \\\\ 248 &=& 2a\left(1-\dfrac{1}{32}\right) \quad & | \quad :2 \\\\ 124 &=& a\left(1-\dfrac{1}{32}\right) \\\\ a\left(1-\dfrac{1}{32}\right) &=& 124 \\\\ a\left(\dfrac{32-1}{32}\right) &=& 124 \\\\ a\left(\dfrac{31}{32}\right) &=& 124 \quad & | \quad \cdot \dfrac{32}{31} \\\\ a &=& 124\cdot \dfrac{32}{31} \\\\ \mathbf{a} & \mathbf{=} & \mathbf{128} \\ \hline \end{array}\)

 

Lara read 128 pages on the first day.

 

 

laugh

 Sep 3, 2018

22 Online Users

avatar