The sum to n terms of an arithmetic progression is given by the formula Sn = n/2 [2a + (n-1)d], where a is the first term and d is the common difference. However, in this case, we are given Sn = 5n^2 + 2n.

To find the nth term of the series, we need to find the difference between the sum to n terms and the sum to (n-1) terms. This is because the nth term is simply the total sum up to n terms minus the total sum up to (n-1) terms.

So, the nth term, An = Sn - S(n-1).

Substituting the given Sn and S(n-1) into the equation, we get:

An = [5n^2 + 2n] - [5(n-1)^2 + 2(n-1)]
= [5n^2 + 2n] - [5n^2 - 10n + 5 + 2n - 2]
= [5n^2 + 2n] - [5n^2 - 8n + 3]
= 5n^2 + 2n - 5n^2 + 8n - 3
= 10n - 3

So, the nth term of the series is 10n - 3. Therefore, the correct answer is (b) 10n - 3.

Question

The sum to n terms of an arithmetic progression is given by the formula Sn = n/2 [2a + (n-1)d], where a is the first term and d is the common difference. However, in this case, we are given Sn = 5n^2 + 2n.

To find the nth term of the series, we need to find the difference between the sum to n terms and the sum to (n-1) terms. This is because the nth term is simply the total sum up to n terms minus the total sum up to (n-1) terms.

So, the nth term, An = Sn - S(n-1).

Substituting the given Sn and S(n-1) into the equation, we get:

An = [5n^2 + 2n] - [5(n-1)^2 + 2(n-1)]
   = [5n^2 + 2n] - [5n^2 - 10n + 5 + 2n - 2]
   = [5n^2 + 2n] - [5n^2 - 8n + 3]
   = 5n^2 + 2n - 5n^2 + 8n - 3
   = 10n - 3

So, the nth term of the series is 10n - 3. Therefore, the correct answer is (b) 10n - 3.

Knowee AI · Accepted Answer

The sum to n terms of an arithmetic progression is given by the formula Sn = n/2 [2a + (n-1)d], where a is the first term and d is the common difference. However, in this case, we are given Sn = 5n^2 + 2n.

To find the nth term of the series, we need to find the difference between the sum to n terms and the sum to (n-1) terms. This is because the nth term is simply the total sum up to n terms minus the total sum up to (n-1) terms.

So, the nth term, An = Sn - S(n-1).

Substituting the given Sn and S(n-1) into the equation, we get:

An = [5n^2 + 2n] - [5(n-1)^2 + 2(n-1)]
   = [5n^2 + 2n] - [5n^2 - 10n + 5 + 2n - 2]
   = [5n^2 + 2n] - [5n^2 - 8n + 3]
   = 5n^2 + 2n - 5n^2 + 8n - 3
   = 10n - 3

So, the nth term of the series is 10n - 3. Therefore, the correct answer is (b) 10n - 3.

The sum to n terms of an arithmetic progression is 5n2 +2n. Find the nth term of the series.a.5n - 2b.10n - 3c.10n + 5d.5n - 1

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