Question

Helppppppppppppp!!!!!

Answer 1

Answer:

Option a is correct. $a_{n}= \frac{2S - a_{1}n}{n}}$

Step-by-step explanation:

Given

$S = \frac{n(a_{1} + a_{n})}{2}$

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

$\frac{2S}{n}=(a_{1} + a_{n})$

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

$\frac{2S}{n} - a_{1}= a_{n}\\\\a_{n} = \frac{2S}{n} - a_{1}$

$a_{n}= \frac{2S - a_{1}n}{n}}$

Answer 2

Answer:

Choice a is correct answer.

Step-by-step 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.