Thread: Arthimetic Series 1

1. It's About Time, in Langley, British Columbia, is Canada's largest custom clock manufacturer. They have a grandfather clock that, on the hours, chimes to the time of day. For example, at 4:00 PM, it chimes 4 times. How many times does the clock chime in a 24-h period?

I tried using the formula Sn = n/2(t1 + tn) and Tn = T1 + (n - 1)d

This is what I did:

Tn = T1 + (n - 1)d

Tn = 1 + (24 - 1)1

Tn = 24

I plugged in 1 for T1 because I assume the first time is 1 PM... I put 24 for n (n = number of terms) because 24 is how many hours there are. And I plugged in 1 for d because I guess the difference is 1.

Sn = n/2(t1 + tn)

S24 = 24/2 (1 + 24)

I plugged in 24 for n (number of terms), 1 for first term, and 24 for tn.

What I did was wrong, and I don't know what to do here...

The correct answer is 156 times.

The series becomes 1+2+3+4+5+.....+ 24
a = 1 n=24 d = 1: Sn = n/2 [ 2a + (n-1) d ] or sum of n natural numbers isgiven by n(n+1)/2
so we get S24 = 24 ( 24+1)/2 = 24*25/2= 12*25 = 300

the answer is 300 as ibdutt found and not 156.

This is a question from a math textbook and I have the answer key, the correct answer to this question is 156 times, not 300 times.

I am sorry for I read the question wrong. It is given that it chimes 4 times at 4 pm whereas I took it as if the clock chimes 16 times at 4 pm.
Now in the light of this revelation the question is simple that it chimes from 1 to 12 times for am and 1 to 12 times for pm.
Thus total number of times for first 12 hours would be 12/2[ 2 + ( 12-1) *1] = 6* 13 = 78 and same number for next 12 hours thus total number would be 78*2 = 156.
Once again sorry for wrong interpretation.

Thank you! I understand now.