Question

arithmetic progression sum. solve ::HOW MANY MULTIPLES OF 4 LIE BETWEEN 10 AND 250? best answer will be marked as brainliest

Answer 1

We know that First multiple of 4 that is greater than 10 is 12. Next will be 16.
Therefore, 12, 16, 20, 24, …
All these are divisible by 4 and thus, all these are terms of an A.P. with first term as 12 and common difference as 4.
When we divide 250 by 4, the remainder will be 2. Therefore, 250 − 2 = 248 is divisible by 4.
The series is as follows.
12, 16, 20, 24, …, 248
Let 248 be the nth term of this A.P.
a = 12
d = 4
an = 248
an = a + (n - 1) d
248 = 12 + (n - 1) × 4
236/4 = n - 1
59  = n - 1
n = 60
Therefore, there are 60 multiples of 4 between 10 and 250

Answer 2

First number after 10 that is divisible by 4 is 12.
So, value of a is 12.

And, The number before 250 which is divisible by 4 is 248

So,

$a_{n} = 248$

$\bf \: the \: value \: of \: a_{2} \: is \: 16$

$d = a_{2} - a_{1} \\ d = 16 - 12 \\ \bf \: d = 4$

n = (to be calculated)

So,

$a_{n} = a + (n - 1)d \\ \\ 248 = 12 + (n - 1)4 \\ \\ 248 = 12 + 4n - 4 \\ \\ 248 = 8 + 4n \\ \\4( 2 + n) = 4(62) \\ \\ 2 + n = \frac{4(62)}{4} \\ \\ 2 + n = 62 \\ \\ n = 62 - 2 \\ \\ n = 60$

Hence, 60 numbers lies between 10 and 250 which are divisible by 4.

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