Question

Helppppppppppppp!!!!!

Answer 1

Choice a is correct answer.

Explanation:

The formula that gives the partial sum of arithematic sequence is

S = n(a₁+aₙ) / 2

We have to find the value of aₙ.

For this, we have to separate aₙ form the given formula.

S = n( a₁+aₙ) / 2

multiplying by 2 to both sides of above equation,we get

2.S = 2.n( a₁+aₙ) / 2

2S = n(a₁+aₙ)

2S = na₁+naₙ

Adding -na₁ to both sides of above equation,we get

2S - na₁ = -na₁+na₁+naₙ

2S - na₁ = naₙ

multiplying by 1/n to both sides of above equation,we get

1/n(2S-na₁) = 1/n(naₙ)

(2S-na₁) / n = aₙ

Rearrange

aₙ = 2S-na₁ / n is the formula to find aₙ.

Answer 2

Option a is correct.
`a_(n)= (2S - a_(1)n)/(n)}`

Explanation:

Given

`S = (n(a_(1) + a_(n)))/(2)`

We have to find the value of
`a_(n)`

Using cross multiplication here

`2S = n(a_(1) + a_(n))`

take n on left hand side

`(2S)/(n)=(a_(1) + a_(n))`

a1 is positive; taking it on the other side will make it negative

`(2S)/(n) - a_(1)= a_(n)\\\\a_(n) = (2S)/(n) - a_(1)`

`a_(n)= (2S - a_(1)n)/(n)}`