Question

how many leap year were there between 1901 and 2000 ?

Answer 1

Leap years b\w 1901 and 2000 are:

1904,1908,1912........2000

By AP

An=2000

2000 = 1904 + (n-1)4

96\4 = n-1

24 +1 = n

n = 25

There were 25 leap years b\w 1901 and 2000.

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Answer 2

Answer:

The number of leap years between 1901 and 2000 =24

Step-by-step explanation:

Required to find,

The number of leap years between 1901 and 2000

Recall the concepts:

All leap years are divisible by 4

The nth term of an AP = $a_n$ = a+(n-1)d, where 'a' is the first term and 'd' is the common difference of the AP

Solution:

The first leap year between 1901 and 2000 =  The first multiple of 4 between 1901 and 2000 = 1904

The last leap year between 1901 and 2000 =  The last multiple of 4 between 1901 and 2000 = 1996

The sequence 1904,1908,1912,...........1996 form an AP, with first term = 1904 and common difference = 4

The nth term of an AP = $a_n$ = a+(n-1)d

Substitute the value of a = 1904, d=4 and  $a_n$ = 1996, in the above equation

1996 = 1904+(n-1)4

1996 -1904 = 4(n-1)

92 = 4(n-1)

n-1 = $\frac{92}{4}$ = 23

n = 23 +1 = 24

The number of terms in the AP  = 24

∴ The number of leap years between 1901 and 2000 =24

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