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Shalnov [3]
3 years ago
11

How many multiples of $6$ are between $100$ and $500$?

Mathematics
2 answers:
lapo4ka [179]3 years ago
7 0

ANSWER

65

EXPLANATION

This will form a sequence with first term:

a_{1} = 102

with constant difference d=6 and last term

l = 486

The last term is a term in the sequence, therefore;

l=a_1+d(n-1)

486=102+6(n-1)

486 - 102 = 6(n-1)

Simplify the LHS

384= 6(n-1)

Divide both sides by 6.

64=n-1

64 + 1 = n

Therefore

n = 65

Hence there are 65 multiples of 6.

sveta [45]3 years ago
5 0

Answer:

67

Step-by-step explanation:

First number between 100 to 500 which is divisible by 6 is 102

Multiples of 6 between 100 to 500 :

102,102+6,102+6+6,....

This Forms an AP

a= first term = 102

d = common difference = 6

Last number between 100 to 500 which is divisible by 6 is 498

So, a_n=498

Formula of nth term = a_n=a+(n-1)d

498=102+(n-1)6

498-102=(n-1)6

396=(n-1)6

\frac{396}{6}=n-1

66=n-1

66+1=n

67=n

Hence there are 67 multiples of 6 between 100 to 500.

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