QUESTION 4
Easy
How many multiples of 4 lie between 10 and 250?
(Hint: All multiples of 4 form an AP. Find the smallest and largest multiples of 4 between 10 and 250.)
SOLUTION
1
Find the first and last term of the AP
First multiple of 4 greater than 10: 12
Largest multiple of 4 less than 250: 248
Largest multiple of 4 less than 250: 248
2
Form the AP
The AP is: 12, 16, 20,..., 248
Here, \(a = 12,\, d = 4,\, l = 248\)
Here, \(a = 12,\, d = 4,\, l = 248\)
3
Find the number of terms
\(l = a + (n − 1)d\)
⇒ \(248 = 12 + (n − 1)4\)
⇒ \(59 = n − 1\)
⇒ \(n = 60\)
⇒ \(248 = 12 + (n − 1)4\)
⇒ \(59 = n − 1\)
⇒ \(n = 60\)
🏆
Final Answer : 60 multiples of 4 lie between 10 and 250.
Concept Note
Multiples of a number form an AP.
To find the number of terms, use
\(n = \frac{l − a}{d} + 1\),
where \(a = \)first term, \(l = \) last term, \(d = \) common difference