Question

how many numbers up to 500, are divisible by 177?
1) 28
2) 30
3) 29
4) 31​

Answer 1

Answer:

2 numbers : 177 and 354.

Step-by-step explanation:

The given case will form AP.

• An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

or

• Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an Arithmetic Progression, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2.

In this AP

• First term: 177

(As 177 is first number which is divisible by 177)

• Common difference: 177

( 2× 177 -177= 177)

( As it's multiple of 177 , hence the difference will be 177)

• Last term : 354.

(354 is largest number divisible by 177 less than 500)

Now,

• Last term =an
• First term = a
• Common difference= d
• Number of terms = n

Then,

an =a+(n-1)d

354 = 177 (n-1) 177

177(n-1) = 354 -177

n-1 = 177 /177

n= 1+1

n= 2.

2 numbers : 177 and 354.

(#SPJ2)