Find the rth term of an A.P.
Question:

Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2.
[Hint: an = Sn – Sn–1]

Solution:

Sum of first n terms be Sn given as Sn = 2n + 3n2

We have to find the rth term that is ar

Using the given hint nth term is given as an = Sn – Sn-1

⇒ ar = Sr – Sr-1

Using Sn = 2n + 3n2

⇒ ar = 2r + 3r2 – (2(r – 1) + 3(r – 1)2)

⇒ ar = 2r + 3r2 – (2r – 2 + 3(r2 – 2r + 1))

⇒ ar = 2r + 3r2 – (2r – 2 + 3r2 – 6r + 3) ⇒ ar = 6r – 1

Hence the rth term is 6r – 1

Long Answer Type

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