The question **"If the sum of nth term of an ap is define as sn=3n2+4 then find the nth term"** is taken from class-10 ** chapter is Arithmetic Progressions Mathematics ** English-Medium

NCERT-Book ➧ class-10 ➧ Mathematics ➧ English-Medium ➧ Arithmetic Progressions ➧ Sum Of N Term Of A.P.

**Question:**

If the sum of n^{th} term of an A.P. is define as S_{n} = 3n^{2} + 4 then find the n^{th} term?

Source:www.questionsbanks.com Last updated: 2022-10-11 23:08:17

**Answer:**

Given that : S_{n} = 3n^{2} + 4

Now Putting n = 1

S_{1} = 3(1)^{2} + 4

= 3 + 4

= 7

Putting n = 2

S_{2} = 3(2)^{2} + 4

= 3 x 4 + 4

= 12 + 4

= 16

a_{1} ≠** **S_{1} ≠ 7

**∵ **a_{1} = S_{1} - S_{0 } Here S_{0} ≠ 0

S_{0} = 3n^{2} + 4 **⇒ **3(0)^{2} + 4 **⇒ **0 + 4 = 4

Using a_{n} = S_{n} - S_{(n - 1)}

a_{1} = S_{1} - S_{0 }

= 7 - 4

= 3

a_{2} = S_{2} - S_{1} [ using formulla a_{n} = S_{n} - S_{(n - 1)} ]

= 16 - 7

= 9

d = a_{2} - a_{1} **⇒ **9 - 3 = 6

a_{n} = a + (n -1)d

= 3 + (n - 1) 6

= 3 + 6n - 6

= 6n - 3

Hence n^{th} term is 6n - 3 **Answer**

**Second Method : **

Given that : S_{n} = 3n^{2} + 4 ................ (i)

Replace n by (n - 1)

We have : S_{n - 1} = 3(n - 1)^{2} + 4

**⇒ ** S_{n - 1} = 3(n^{2} - 2n + 1) + 4

= 3n^{2} - 6n + 3 + 4

= 3n^{2} - 6n + 7 ......................... (ii)

a_{n} = S_{n} - S_{(n - 1) }

= 3n^{2} + 4 - (3n^{2} - 6n + 7 )

= 3n^{2} + 4 - 3n^{2} + 6n - 7

= 6n - 3 **Answer **

1 Questions Found on same Topics.

If the sum of n^{th} term of an A.P. is define as S_{n} = 3n^{2} + 4 then find the n^{th} term?

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All chapters of NCERT Book as ncert solutions have exercise questions, textual questions and so many addtional questions like short answered questions, long answered questions and very long questions, here we included all types of questions answers format that need for a students and other stock holders like teachers and tutors. If the sum of nth term of an ap is define as sn=3n2 4 then find the nth term - Questions Bank is from NCERT Solutions class 10 English-Medium subject Mathematics chapter- Arithmetic Progressions Questions bank

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