Question

Find the sums of all two digit
odd positive numbers​

Answer 1

$\bf{\underline{Solution}}:-$

➟ All two digit odd positive numbers are 11,13,15,17,.........,99.

This is an Arithmetic progression (AP).

Given :-

• First term (a) = 11

• Common difference (d) = 13 - 11 = 2

• Last term (L) = 99

To find :-

• Required sum

Solution :-

Let the number of terms be n

we know that,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{T_n=a+(n-1)d}}}}$

$\rm\longrightarrow\:99=11+(n-1)\times{2}$

$\rm\longrightarrow\:99-11=(n-1)\times{2}$

$\rm\longrightarrow\:88=(n-1)\times{2}$

$\rm\longrightarrow\:\cancel\dfrac{88}{2}=(n-1)$

$\rm\longrightarrow\:44=(n-1)$

$\rm\longrightarrow\:44+1=n$

$\rm\longrightarrow\:45=n$

$\rm\longrightarrow\:n=45$

Then,

we know that,

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\pink{s=\dfrac{n}{2}(a+L)}}}}$

$\rm\longrightarrow\:s=\dfrac{45}{2}(11+99)$

$\rm\longrightarrow\:s=\dfrac{45}{\cancel{2}}\times\:\cancel{110}\:\:\:\:\:55$

$\rm\longrightarrow\:s=45\times{55}$

$\rm\longrightarrow\:s=2475$

Hence,the required sum will be 2475.