Question

Find the sum of 3+11+19+...+803

Answer 1

Solution : -

3 + 11 + 19 + ... + 803

This is in the form Arithmetic Progression.

So We Can Use the Equation in A.P to find Sum .

$S = \frac{n}{2} [ a + a_{n} ]$

Here, a = 3 , $a_{n} = 803$ and we need to find n = ?

So, to find n , we will use the formula ... $a_{n} = a + (n - 1 ) d$

Here, d is common Difference , where d = 11 - 3 = 19 - 11 = 8

So by using above formula ,

803 = 3 + ( n - 1 ) 8

800 = ( n - 1 ) 8

n - 1 = 800/8

n = 101

So, now sum is

S = $\frac{101}{2} [ 3 + 803 }$

S = 101 * 403

S = 40,703

Therefore , 3 + 11 + 19 + ... + 803 = 40,703

Answer 2

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