Question

find an of 4n - n sq

Answer 1

Answer:

4n is the answer because n-n square =n so, 4n is the answer

Answer 2

Given

• Sum of A.P = 4n - n²

Since It is the sum of n terms. We put n = [1,2,3,......,n]

So,

Case 1:

n = 1

Sum of first term = 4 × 1 - 1²

=> 3

Since sum of first term of an A.P is the first term itself because we aren't adding anything to it.

•°• a = 3 (1)

Case 2:

n = 2

Sum of first two terms = 4 × 2 - 2²

=> 8 - 4

=> 4 (2)

We know that standard from of A.P is a, a+d, a+2d , ... , a + (n-1)d

Therefore, Sum of first two would be:

=> a + a + d = 4 [ from eq.(2) ]

=> 2a + d = 4

=> 2 × 3 + d = 4 [ a = 3 from eq.(1) ]

=> d = 4 - 6

=> d = -2 (3)

From the standard form of A.P, we know that an A.P is of the form a , a+d , a+2d , ... , a + (n-1)d , We have our A.P:

=> a , a+d , a+2d , ... , a+(n-1)d

=> 3 , 3 + (-2) , 3 + 2(-2) , ... , 3 - 2n + 2

=> 3 , 3 - 2 , 3 - 4 , ... , 3 + 2 - 2n

=> 3 , 1 , -1 , ... , 5 - 2n

Answer:

$\bold{3\: , \: 1 \: , \: -1 \: , \: \ldots \: , \: 5\: - \:2n}$