Question

how many multiples of 6 lie between 100 and 300 using the A.P method​

Answer 1

Answer:

35

Step-by-step explanation:

They are, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300.

Answer 2

There Are 34 Multiples Of 6 Between 100 And 300

GIVEN

Number Range - 100-300

TO FIND

Numbers of multiple of 6 between 100 and 300 using the A.P method.

SOLUTION

We can simply solve the above problem as follows-

Given,

Number Range = 100 - 300

Let us divide 100 by 6 to find the first number as a multiple of 6.

By dividing, 100 by 6, we get 17 as a quotient.

First multiple of 6 = 17×6 = 102

So,

The first multiple of 6 = 102.

The last multiple of 6 = 300

Using the Formula for the arithmetic mean progression,

an = a1 + (n-1)d

Where,

an = The nth term in the sequence

a1 = First term

d = common difference

n = number of terms

Putting the values in the above formula we get,

300 = 102 + (n-1)6

300-102 = (n-1)6

198 = (n-1)6

198/6 = n-1

33 = n-1

33 + 1 = n

34 = n

Hence, there are 34 multiples of 6 between 100 and 300

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