Question

Find the sum of all natural numbers
between 200 and 300 which are exactly
divisible by 6.​

Answer 1

Step-by-step explanation:

Starting no. Which is divisible by 6= 204

Then a=204

n=no. Of total terms =16

d=6

l=300

S=(a+l)n/2

=(204+300)8=8*504=4032

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Answer 2

Given ,

The AP is 204 , 210 , 216 , ... , 294

Here ,

First term (a) = 204

Common difference (d) = 6

Last term (an) = 294

We know that , the general formula of an AP is given by

$\sf \star \: \: a_{n} = a + (n - 1)d$

Thus ,

$\Rightarrow \sf 294 = 204 + (n - 1)6 \\ \\ \Rightarrow \sf </p><p>90 = (n - 1)6 \\ \\ \Rightarrow \sf </p><p>n - 1 = 15 \\ \\ \Rightarrow \sf </p><p>n = 16</p><p>$

Now , the sum of first n terms of an AP is given by

$\star \: \: \sf S_{n} = \frac{n}{2} (a + l)$

Thus ,

$\Rightarrow \sf S_{16} = \frac{16}{2} (204 + 294) \\ \\\Rightarrow \sf S_{16} = 8 \times 498 \\ \\\Rightarrow \sf S_{16} = 3984$

$\therefore \sf \bold{ \underline{The \: sum \: is \: 3984}}$