Question

The sum of all even numbers between 10 and 90.​

Answer 1

The sum of all even numbers between 10 and 90 is 2050.

Given:

Even numbers from 10 to 90.

To Find:

The sum of all even numbers between 10 and 90.​

Solution:

The even numbers between 10 and 90 are:

10, 12, 14, 16 ......., 90

So,

Sum = 10+12+14+……+90

=> 2(5+6+7+….+45)

=>  2(1+2+3+4+5+6+7+….+45)–2(1+2+3+4))

=> 2 *[(1/2)*45*(45+1)-(10)]

=> 2 *[(1/2)*45*(46)-10]

=> 2*1025

=> 2050

Hence, The sum of all even numbers between 10 and 90 is 2050.

#SPJ3

Answer 2

Answer:

The sum of all even numbers between 10 and 90 = 1950

Step-by-step explanation:

To find,

The sum of all even numbers between 10 and 90

Recall the formula,

The number of terms of an AP,

n = $\frac{a_n - a}{d} +1$

The sum to n - terms of an AP,

Sₙ = $\frac{n}{2}( a+a_n)$

Where 'a' is the first term of AP, and 'd' is the common difference and 'aₙ' is the last term of the AP.

Solution:

Let A be the set of all even numbers between 10 and 90.

Sum of all even numbers between 10 and 90

Since the common difference of this set of numbers is 2, these numbers form an AP with first term 12, and last term 88

The number of terms in this AP

=  $\frac{a_n - a}{d} +1$

= $\frac{88 - 12}{2} +1$

= $\frac{76}{2} +1$

= 38 + 1

= 39

Hence we have, there are 39 terms in this AP.

That is, there are 39 even numbers between 10 and 90

Sum of all even numbers between 10 and 90 = S₃₉

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

= $\frac{39}{2}( 12+88)$

= $\frac{39}{2}(100)$

= 39×50

= 1950

∴ The sum of all even numbers between 10 and 90 = 1950

#SPJ2