Question

Find the number of terms between 200 and
700, which are divisible by 15. Find the sum
of these terms.
(Hint : First term = 210
last term = 690, d = 15)​

Answer 1

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Your Answers are,

$\text{\large\underline{\pink{Number of ton:-:-}}}$

• ⠀⠀$\bold{First\: term\: (a)\: = 210}$

• ⠀⠀$\bold{Last\: term \:(l)\:= 690}$

• ⠀⠀$\bold{Common\: Difference\: (d) = 15.}$

$\text{\large\underline{\green{To find}}}$

• ⠀⠀$\bold{Number \:of terms \:(n)}$

• ⠀⠀ $\bold{Summer\: of \:the\: terms (Sn)}$

Formula Used:-

⠀⠀⠀⠀$\begin{gathered}\\ \red{\longrightarrow \boxed {\green{ \bf l = a + (n - 1)d}}}\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \red{\longrightarrow \boxed {\green{ \bf Sn = \frac{n}{2} + \bigg(a + l \bigg)}}}\end{gathered}$

Where,

• ⠀⠀⠀$\bold{l \:=\: Last \:term}$

• ⠀⠀⠀$\bold{a\: = \:First\: term}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ⠀⠀⠀$\bold{n\: =\: Number \:of\: terms}$

• ⠀⠀⠀$\bold{Sn\: = Sum \:of \:n\: terms}$

Now,

By putting the values in first formula we get,

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto 690 = 210 + (n - 1)15\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto 690 = 210 + 15n - 15\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto 15n = 690 - ( 210 - 15)\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto 15n = 690 - 195\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto15n = 495\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto n = \cancel\frac{495}{15}\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \large\red{\mapsto \boxed {\blue{ \bf n = 33.}}}\end{gathered}$

⠀⠀⠀⠀$\boxed{\blue{\boxed{\textbf{ \therefore Number of terms is n = 33}}}}$

Again,

By putting values in second formula we get,

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto S_{33}= \frac{33}{2} \bigg(210 + 690 \bigg)\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto S_{33}= \frac{33}{ \cancel2} \bigg( \cancel{900} \: \: {}^{450} \bigg)\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \tt\mapsto S_{33}= 33 \times 450\end{gathered}$

⠀⠀⠀⠀$\begin{gathered}\\ \large\red{\mapsto \boxed {\blue{ \bf S_{33}= 14850}}}\end{gathered}$

$\boxed{\purple{\boxed{\textbf{ \therefore Sum Of these terms = 14850}}}}$

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Answer 2

Therefore Sum Of these terms = 14850