Question

Number of 4 multiples between 10 and 250 are_____. Pls explain it just don't type the answer. Tell me how you got it​

Answer 1

Basic Concept Used :-

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ nᵗʰ term of an arithmetic sequence is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

• aₙ is the nᵗʰ term.

• a is the first term of the sequence.

• n is the no. of terms.

• d is the common difference.

$\large\underline{\sf{Solution-}}$

Multiples of 4 lying between 10 and 250 are

• 12, 16, 20, ----------, 248

It forms an AP series, whose

• First term, a = 12

• Common difference, d = 16 - 12 = 4

• Last term, aₙ = 248

Let number of terms be n.

We know that,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

On substituting the values of aₙ, a and d, we get

$\rm :\longmapsto\:248 = 12 + (n - 1) \times 4$

$\rm :\longmapsto\:248 - 12 = (n - 1) \times 4$

$\rm :\longmapsto\:236 = (n - 1) \times 4$

⇛ n - 1 = 59

⇛ n = 59 + 1

⇛ n = 60.

Hence,

• There are 60 numbers in between 10 and 250 which are divisible by 4.