Question

in an AP th the sum of n terms is given by sn=n2-3n find the 30 th term​

Answer 1

Hey! I'd be glad to help you with this.

Answer:

56

Step-by-step explanation:

If we sum up a series upto n variables then subtracting the sum of the same series till (n - 1) we get the last variable of the series .

In this AP , the sum of n terms is

Sn = n² - 3n

Therefore the sum of (n-1) terms will be

S(n -1) = (n - 1)² - 3(n - 1)

The last term of the series = Sn - S(n- 1)

= n²- 3n - { (n - 1)² - 3(n - 1)}

simplifying it further by expanding (n-1)² and removing the parenthesis:-

= n² - 3n - { n² + 1 - 2n - 3n + 3}

= [n²] + [- 3n] - [n²] - 1 + 2n + [+ 3n] - 3

= 2n - 4

(the terms within [.] get canceled)

So, the last term of this series (nth term) is

(2n - 4)

substituting n with 30, to get the 30th term of this series:-

(2 × 30 - 4)

= 60 - 4

= 56

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Hope this helps !

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