Question

Find the sum of all even integers 12 to 864,inclusive.

Answer 1

Answer:

the sum of all the even integers from 12 to 864, inclusive is 187,026.

Step-by-step explanation:

12,14,16,18,20.........864

a1=12

d=14-12  =2

an=864

an = a1 + (n-1)d

864 =

12 + ( n-1)2

864 =12 + 2n -2

864 = 10 + 2n

-10 + 864 = 2n

854/2 = 2n/2

854/2 = n

n = 427

Sn = n/2 (a1+an)

S427 = 427/2 (12 + 864 )

         = 213.5  (876)

S427 = 187,026

Sum of all even integers from 12 to 864 is 187,026.

Answer 2

Given:

first term = 12

last term = 864

To find:

the sum of all the even numbers in the range

Solution:

The even numbers from 12 to 864 form an A.P. series:

12, 14, 16, 18,..., 864.

Now the first term of the series = $a_1$ = 12

the last term of the series = $a_n$ = 864

the common difference = $d$ = 14-12 = 2

We know that,

$a_n=a_1+(n-1)d$

where, $n$ is the number of terms.

Putting the values,

$864=12+(n-1)$×$2$

⇒$(n-1)=\frac{864-12}{2}$

⇒$n=427$

Now, to find the sum we can use the formula

$S_n=\frac{n}{2} (a_1+a_n)$

Putting the values,

$S_n=\frac{427}{2}$×$(12+864)$

$=\frac{427}{2}$×$876$

$=187026$

Hence, the sum of all the even integers from 12 to 864 is 187,026.