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+4 votes
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in Mathematics by (51.7k points)
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The sum of the first n terms of an AP is given by Sn, = 3n2 - 4n. Determine the AP and the 12th term.

2 Answers

+1 vote
by (17.0k points)
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Best answer

The sum of first n term is 3n2 - 4n

The sum of first n - 1 term is 3(n - 1)2 - 4(n - 1)

The difference of sum of (n – 1) and n will give us the value of an

The value of an = 6n - 7

Putting the value of n = 1, 2 to determine the first value of the series and the common difference

a1 = 6 x 1 - 7; a1 = -1

a2 = 6 x 2 - 7; a2 = 5

d = a2 - a1

= 5 - (-1)

= 6

Now to find the 12th term of series we use the formula of Arithmetic Progression:

a12 = a1 + (12 - 1)d

a12 = -1 + (11)6

a12 = -1 + 66

a12 = 65

Therefore, the value of 12th term of series is 65, whereas the value of nth term of series is 6n - 7.

+4 votes
by (266k points)

Answer is.....

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