Question

For an AP, if Sn if Sn = 3n2 - 4n, 3n2 - 4n, then an = 6n- 7.​

Answer 1

Step-by-step explanation:

Given Sum of n terms is Sn=3n2−4n

So Sum of n−1 terms is Sn−1=3(n−1)2−4(n−1)

=3n2−6n+3−4n+4

=3n2−10n+7

Sum of n terms is equal to sum of n−1 terms plus nth term

⟹nth term =Sn−Sn−1=3n2−4n−(3n2−10n+7)

nth term=6n−7 

Answer 2

Answer:

Given below is the answer

Step-by-step explanation:

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence. For example, the series of natural numbers: 1, 2, 3, 4, 5, 6,… is an Arithmetic Progression, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1). Even in the case of odd numbers and even numbers, we can see the common difference between two successive terms will be equal to 2.

Given Sum of n terms is Sn=3n2−4n

So Sum of n−1 terms is Sn−1=3(n−1)2−4(n−1)

=3n2−6n+3−4n+4

=3n2−10n+7

Sum of n terms is equal to sum of n−1 terms plus nth term

⟹nth term =Sn−Sn−1=3n2−4n−(3n2−10n+7)

nth term=6n−7

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