Question

find the sum of all positive integers less than 298 which are multiples of 9

Answer 1

Given that ,

The AP is 9 , 18 , 27 .... 297

Here ,

First term (a) = 9

Common difference (d) = 9

Last term (l) = 297

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

$\large \sf \fbox{ a_{n} = a + (n - 1)d}$

Thus ,

➡297 = 9 + (n - 1)9

➡288 = (n - 1)9

➡32 = n - 1

➡n = 33

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

$\large \sf \fbox{S_{n} = \frac{n}{2} \{2a + (n - 1)d \}}$

Thus ,

$\sf \Rightarrow S_{33} = \frac{33}{2} \{2 \times 9 + (33 - 1)9 \} \\ \\ \sf \Rightarrow S_{33} = \frac{33}{2} \times (18 + 288) \\ \\ \sf\Rightarrow S_{33} = \frac{33}{2} \times 306 \\ \\ \sf \Rightarrow S_{33} =33 \times 153 \\ \\ \sf \Rightarrow S_{33} = 5049$

$\sf \therefore\underline{The \: required \: value \: is \: 5049}$

Answer 2

answer 5049

hope this answer helps you