Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2.[

1.	Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2.[Hint: an = Sn – Sn–1]
Answer» Sum of first n terms be S_n given as S_n = 2n + 3n² We have to find the r^th term that is a_r Using the hint: the n^th term is given as a_n = S_n – S_n-1 ⇒ a_r = S_r – S_r-1 Using S_n = 2n + 3n² ⇒ a_r = 2r + 3r² – (2(r – 1) + 3(r – 1)²) ⇒ a_r = 2r + 3r² – (2r – 2 + 3(r² – 2r + 1)) ⇒ a_r = 2r + 3r² – (2r – 2 + 3r² – 6r + 3) ⇒ a_r = 6r – 1 Hence the r^th term is 6r – 1

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

Answer»

Sum of first n terms be S_n given as

S_n = 2n + 3n²

We have to find the r^th term that is a_r

Using the hint: the n^th term is given as a_n = S_n – S_n-1

⇒ a_r = S_r – S_r-1

Using S_n = 2n + 3n²

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

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

⇒ a_r = 2r + 3r² – (2r – 2 + 3r² – 6r + 3)

⇒ a_r = 6r – 1

Hence the r^th term is 6r – 1