Question

How many natural numbers lie between 59 square and 60 square?

Answer 1

Answer:

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Answer 2

Answer:

The number of natural numbers lies between 59² and 60² = 118

Step-by-step explanation:

Required to find

The number of natural numbers lies between 59² and 60²

Recall the formula

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

Solution

59² = 3481

60² = 3600

The natural numbers lie between 59² and 60² are

3482, 3483, 3484, .............3599

The number of natural numbers lie between 59² and 60² = the number of elements in the set {3482, 3483, 3484, .............3599}

The set 3482, 3483, 3484, .............3599 form an AP,

with first term  = a = 3482

common difference =d = 1

We need to find 'n' such that $a_n = 3599$

a+(n-1)d = 3599

3482+(n-1)  = 3599

n-1 = 3599 - 3482

n-1 = 117

n = 117+1

= 118

n = 118

∴The number of natural numbers lies between 59² and 60² = 118

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