Question

what is the nth term of an arithmetic progression whose sum to 'n' terms is 2n^2 - 3n?​

Answer 1

Answer:

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Answer 2

Concept:

aₙ = Sₙ - Sₙ₋₁

Given:

Sum of n terms = 2n² - 3n

Find:

The nth term.

Step-by-step explanation:

Sum of n terms = 2n² - 3n

Sum of n - 1 terms will be:

Sₙ₋₁ = 2 ( n - 1)² - 3( n - 1)

Sₙ₋₁ =2n² + 2 - 4n - 3n + 3

Sₙ₋₁ =2n² - 7n + 5

Now the nth term will be

Sₙ - Sₙ₋₁ = 2n² - 3n - (2n² - 7n + 5)

Sₙ - Sₙ₋₁ = 2n² - 3n - 2n² + 7n - 5

Sₙ - Sₙ₋₁ = 4n - 5

aₙ = 4n - 5

Therefore, we get the nth term as 4n - 5.

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