Question

Calculate the sum of odd numbers between $300$ and $450$ which are divisible by $15$.

• A. $3,794$
• B. $3,710$
• C. $3,302$
• D. $3,375$

Answer 1

The correct option is D $3,375$

The even numbers between $300$ and $450$ which are divisible by $15$ are $315,330,......435$

The sum of first $n$ terms of arithmetic series formula can be written as,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ ............ (1)

Where $n=$ number of terms = ?

$a=$ first odd number $=315$

$d=$ common difference of A.P. $=15$

$T_n=$ Last term $=435$

$T_n=a+(n-1)d$

$435=315+(n-1)15$

$435=315+15n-15$

$435-315+15=15n$

$135=15n$

$n=9$

Apply the given data in the formula (1),

$S_9=\frac{9}{2}[2\times 315+(9-1\left)15\right]$

$=4.5[630+(8\left)15\right]$

$=4.5[630+120]$

$=4.5\left[750\right]$

$=3,375$

So, the sum of odd numbers between $300$ and $450$ which are divisible by 15 is 3,375.