If Sn =2n²-7n, then the nth term is (a) 4n+9 (b) 2n +3 4n-9 (c) 4n-9 (d) 9-4nplease answer with explanation

Subject:
CBSE BOARD X
Author:
germansosa
Created:
1 year ago

Answers 2

Answer:

(b) 2n+3 4n-9 i think that by me

Author:

babyfbji
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Answer:

The nth term = 4n - 9

Explanation:

A sequence of numbers where the difference between every two consecutive numbers is a constant is called an arithmetic progression (AP).

[tex]a_{1} , a_{1}+d, a_{1}+2d, a_{1}+3d,....[/tex]

nth term of an AP is given by:

[tex]a_{n} =a_{1} +(n-1)d[/tex]

where a₁ is the first term and d the common difference.

Step 1:

We have been given the sum of n terms of the AP:

Sₙ = 2n² - 7n

Sum of first term, S₁ = a₁

S₁ = 2×1² - 7×1 = -5

∴ a₁ = -5

Sum of first two terms, S₂ = a₁ + a₂

S₂ = 2×2² - 7×2 = -6

a₁ + a₂ = -6

a₂ = -6 - (-5)

∴ a₂ = -1

Sum of first two terms, S₃ = a₁ + a₂ + a₃

S₃ = 2×3² - 7×3 = -3

a₁ + a₂ + a₃ = -3

a₃ = -3 - (-5) - (-1)

∴ a₃ = 3

Therefore, the series is: -5, -1, 3,.....

Step 2:

The difference of two consecutive terms gives the common difference d:

a₂ - a₁ = -1 - -5 = 4

a₃ - a₂ = 3 - -1 = 4

∴ d = 4

Step 3:

The nth term of an AP is given by:

aₙ = a₁ + (n - 1)d

aₙ = -5 + (n - 1)×4

aₙ = -5 + 4n - 4

aₙ = 4n - 9

Author:

kaelmckay
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If Sn =2n²-7n, then the nth term is (a) 4n+9 (b) 2n +3 4n-9 (c) 4n-9 (d) 9-4nplease answer with explanation

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Other CBSE BOARD X Questions

If Sn =2n²-7n, then the nth term is (a) 4n+9 (b) 2n +3 4n-9 (c) 4n-9 (d) 9-4nplease answer with explanation​

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Other CBSE BOARD X Questions

If Sn =2n²-7n, then the nth term is (a) 4n+9 (b) 2n +3 4n-9 (c) 4n-9 (d) 9-4nplease answer with explanation