Question

Set a contains all the even numbers between 2 and 50 inclusive. Set b contains all the even numbers between 104 and 152 inclusive. What is the difference between the sum of elements of set b and that of set a?

Answer 1

Answer:

the difference between the sum of element of set b and that of set a is 54

Answer 2

Given,

Set A: All even numbers from 2 to 50 both inclusive,

Set B: All even numbers from 104 to 152 both inclusive.

To find,

Difference between the sum of elements of both sets.

Solution,

The difference between the sum of elements of the given two sets can be found by applying firstly, the formula for the sum of A. P. to both. Then the obtained sums can be simply subtracted.

Now, the sets A and B will be

A = {2, 4, 6, 8, 10, ..., 50}

B = {104, 106, 108, ..., 152}

Here, it can be observed that the number of terms in both of the sets will be 25.

Now, for A. P. in set A,

a = 2, d = 2, n = 25

Applying the sum of the A. P. formula,

$S_n=\frac{n}{2} [2a+(n-1)d]$

$S_n=\frac{25}{2} [2(2)+(25-1)2]$

$S_n=\frac{25}{2} [4+(24)2]$

$S_n=\frac{25}{2}\times 52$

$S_n = 650$

For A. P. in set B,

a = 104, d = 2, n = 25.

$S_n=\frac{25}{2} [2(104)+(25-1)2]$

$S_n=\frac{25}{2} [(208)+(24)2]$

$S_n=\frac{25}{2} \times 256$

$S_n =3200$

The difference between both the sums = 3200 - 650

= 2550.

Therefore, the difference between the sum of elements of set B and that of set A will be 2550.