Question

Numbers between 100 and 200 which are divisible by 6 are

Answer 1

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

Let's first find the numbers between 100 and 200 which are divisible by 6, we get

$\rm :\longmapsto\:102, \: 108, \: 114, \: - - - - ,198$

$\bf\implies \:Its \: an \: AP \: series \:$

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.

Tʜᴜs,

Here,

• First term, a = 102

• Common difference, d = 6

• nᵗʰ term of series, aₙ = 198

• Let number of terms be 'n'.

On substituting the values in formula,

$\rm :\longmapsto\:\begin{gathered}{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}\\ \end{gathered}$

$\rm :\longmapsto\:198 = 102 + (n - 1)6$

$\rm :\longmapsto\:198 - 102 = (n - 1)6$

$\rm :\longmapsto\:96 = (n - 1)6$

$\rm :\longmapsto\:16 = (n - 1)$

$\bf\implies \:n = 17$

Additional Information :-

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ Sum of first n terms of an arithmetic sequence is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{S_n\:=\dfrac{n}{2} \bigg(\:2a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

• Sₙ is the sum of first n terms.

• a is the first term of the sequence.

• n is the no. of terms.

• d is the common difference.