Question

16. If a clock strikes once at 1 o’clock, twice at 2 o’clock and so on, how many times will
it strike in a day?

Answer 1

a clock strikes once at 1 o' clock , twice at 2 o' clock and so on.
we have to find out number of strikes in a day .

Do you know, in a day there are 24 hours ?
But a clock made for 12 hours . Means, we have to multiply two times to sum of stikes upto 12 hours .
so, clock strikes serially , 1 , 2 , 3, 4 , ...... 12

here what you observed?
all are in AP because common difference is always 1 .
Now, use sum of n natural number = n(n+1)/2
Here, n = 12
∴ clock strikes in 12 hours = 12(12 + 1)/2 = 78
∴ clock strikes in a day = 2 × 78 = 156

Hence, answer is 156

Answer 2

General term or nth term of A.P
The general term or nth term of A.P is given by an or tn = a + (n – 1)d, where a = a1 is the first term, d is the common difference and n is the number of term.

Sum of n terms of an AP
The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by
Sn = n /2 [ 2a + ( n - 1) d] or
Sn=n /2 [ a + l ] (l = last term)

SOLUTION :
GIVEN :
The clock strikes once at 1 o'clock,twice at 2 o'clock and so on.
[1 day = 24 hours] clock has 12 hours so we have to multiply the series by 2 to make it 24 hours.

2 [1 + 2 + 3 + ............ + 12]

Sn=n /2 [ a + L ]
Here, a = 1, n = 12, L = 12

S12 = 2 x (n/2) [a+L]
S12= 2 x (12/2) [1+12]
S12 = 12 × 13
S12 = 156

Hence, the clock will strike 156 times in a day.

HOPE THIS WILL HELP YOU...