Question

the algebraic expression of a sequence is 81-8n wheather the sum of any number of terms of the sequence will be 400.Why??? ​

Answer 1

Answer:

400

Step-by-step explanation:

If n=50

Then 81-(8×50)=81-400

According to problem we add any number so add 81 then

=81-(400+81)

=81_481

Change symbols then

=-81+481

=400.

Answer 2

400 will not be sum of any number of terms in given Sequence

Given:

The algebraic expression of a sequence is 81-8n

To find:

check whether the sum of any number of terms is 400

Solution:

Given the algebraic expression of a sequence is 81-8n

Take n = 1 ⇒ 1st term a = 81 - 8(1) = 73

Take n = 2 ⇒ 2nd term a₂ = 81 - 16 = 65

⇒ Common difference d = a₂ - a = 65 - 73  = - 8

Let at nth term the sum of the terms = 400

As we know sum of n terms = $\frac{n}{2} [ 2a + (n-1)d ]$  

⇒  $\frac{n}{2} [ 2a + (n-1)d ]$ =  400  

⇒  $\frac{n}{2} [ 2(73) + (n-1)(-8) ] = 400$

⇒ n [ 146 - 8n + 8 ] = 800

⇒ n [ 154 - 8n ] = 800

Here the above equation it not true for any value of n value

So here, we can conclude that 400 will not be sum of any number of terms in given Sequence

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