Question

From 232 to 540, find the number of multiples of 3.

Answer 1

1. Identify the first multiple

A multiple of 3 is a number where the sum of its digits is divisible by 3.

Testing 232: 2 + 3 + 2 = 7   ...(Not divisible by 3)

Testing 233: 2 + 3 + 3 = 8   ...(Not divisible by 3)

Testing 234: 2 + 3 + 4 = 9   ...(Divisible by 3)

The first term (a) is 234.

2. Identify the last multiple

Testing 540: 5 + 4 + 0 = 9   ...(Divisible by 3)

The last term (L) is 540.

3. Apply the arithmetic progression formula

The number of terms n in an arithmetic sequence can be found using the formula:

`n = (L - a)/d + 1`

Where:

L = 540   ...(Last term)

a = 234   ...(First term)

d = 3   ...(Common difference)

`n = (540 - 234)/3 + 1`

`n = 306/3 + 1`

n = 102 + 1

n = 103

There are 103 multiples of 3 from 232 to 540.