Question

Sn = 3n² - 2n of an AP, find an.

Answer 1

Answer:

here is your answer

Step-by-step explanation:

S

n

=3n

2

+2n

Taking n=1, we get

S

1

=3(1)

2

+2(1)

⇒S

1

=3+2

⇒S

1

=5

⇒a

1

=5

Taking n=2, we get

S

2

=3(2)

2

+2(2)

⇒S

2

=12+4

⇒S

2

=16

∴a

2

=S

2

−S

1

=16−5=11

Taking n=3, we get

S

3

=3(3)

2

+2(3)

⇒S

3

=27+6

⇒S

3

=33

∴a

3

=S

3

−S

2

=33−16=17

So, a=5,

d=a

2

−a

1

=11−5=6

Now, we have to find the 15

th

term

a

n

=a+(n−1)d

a

15

=5+(15−1)6

a

15

=5+14×6

a

15

=5+84

a

15

=89

Hence, the 15

th

term is 89 and AP is 5,11,17,23,...

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