Question

Find the sum of all two digit odd multiples of 3?
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Answer 1

find the sum of all two digit odd multiple of3?

Answer 2

Answer:

Step-by-step explanation:

Two digit odd multiples of 3 numbers are =15,21,27,33,39,45,51,57,63,69,75,81,87,93,99

therefore,

the sum of the number

$S_{n}=\frac{n}{2}(2\times n+(n-1)\times d)$

Where, n=No. of terms=15

d= difference between two consecutive number=6

$\therefore S_{n}=\frac{n}{2}[2\times n+(n-1)\times d]\\\\\Rightarrow S_{n}=\frac{15}{2}[2\times 15+(15-1)\times 6]\\\\\Rightarrow S_{n}=\frac{15}{2}[30+(14\times 6)]\\\\\Rightarrow S_{n}=\frac{15}{2}[30+84]\\\\\Rightarrow S_{n}=\frac{15}{2}\times 114$

$\\\\\Rightarrow S_{n}=855$