Question

How many multiples of 5 are there in between 100 and 300?

Answer 1

Solution given:

first term [a]=100

last term[l]=300

common difference [d]=5

second term[b]=100+5=105

now

we have

l=a+(n-1)d

substituting value

300=100+(n-1)5

300-100=(n-1)5

200/5=n-1

40=n-1

n=40+1

there are 41 multiple in between 100 and 300/including it but no including its 41-2=39 multiple

Answer 2

• 39 multiples

Explanation:

Consider AP:

• 105, 110, ..., 295

As multiples of 5 between 100 and 300

The first term is 105, the common difference is 5, the last term is 295.

Use the nth term formula:

• 105 + 5(n - 1) = 295
• 5(n - 1) = 190
• n - 1 = 190/5
• n - 1 = 38
• n = 39