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If Sn, the Sum of First N Terms of an Ap is Given by Sn = 3n2 - 4n, Find the Nth Term. - Mathematics

Sum

If Sn, the sum of first n terms of an AP is given by Sn = 3n2 - 4n, find the nth term.

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Solution

We have, Sn = 3n2 - 4n
for n = 1 ⇒ `S_1 = 3 (1)^2 - 4(1) = 3 - 4 = -1`
⇒ a1 = S1 = -1
for n = 2 ⇒ `S_2 = 3(2)^2 - 4(2)`
= 12 - 8 = 4
`S_2 = 4`
a2 = S2 - S2
= 4 -(-1)
a2 = 5

Common difference, d = a2 - a1
d = 5 -(-1)
d = 6
⇒ an = a + (n -1)d
= (-1) + (n -1)6
= -1 + 6n - 6
an = 6n - 7
⇒ nth term is (6n - 7)

Concept: Algebraic Conditions for Number of Solutions
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