Answer to Question #164631 in Algebra for emma

Question

depth of 2 digit 10 to 99

Answer 1

Number of digits from 10 to 99 is 90

and sum of digits from 10 to 99 is=

$S_{n}= \dfrac{n}{2}(2a + (n-1)d)$

Here,

n= 90

a= 10

d= 1

So, $S_{90}= \dfrac{90}{2}((2\times 10)+ 89\times1)$

$S_{90}= 45(20+ 89)= 45\times109$

$= 4905$

Hence, Sum of digits from 10 to 99 is 4905