Question

the sum of the first n terms of an AP is given by
$sn = 3n ^{2} - n$
determine the AP and the 25th term

Answer 1

Heya!

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Sn = 3n² - n

S1 = 3 (1)² - 1
S1 = 3 - 1
S1 = 2

First term is 2

S2 = 3 (2)² - 2
S2 = 12 - 2
S2 = 10

a2 = S2 - a1
a2 = 10 - 2
a2 = 8

d = a2 - a1
d = 8-2
d = 6

A.P = 2 , 8 , 14 ....

Now, what's the 25th term?

an = a + (n-1)d
a25 = 2 + (25 - 1) 6
a25 = 2 + 24 × 6
a25 = 2 + 144
a25 = 146

Thus, the 25th term is 146.


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Hope it helps...!!!