Home
NCERT Soltions
Class 11
Mathematics
Sequence and Series
Find the sum to n terms of the series 3 × 12 + 5 ...

Find the sum to n terms of the | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

Answer:

The given series is 3 ×1² + 5 × 2² + 7 × 3² + …

nth term, a_n = ( 2n + 1) n² = 2n³ + n²

^{$therefore space S subscript n space end subscript equals space sum from k equals 1 to n of space a subscript k space space space space space space space space space space space space equals space sum from k equals 1 to n of space open parentheses 2 k cubed space plus space k squared close parentheses space equals space 2 sum from k equals 1 to n of space k cubed space plus space sum from k equals 1 to n of space k squared space space space space space space space space space space space space equals space 2 open square brackets fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction close square brackets squared space plus space fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction space space space space space space space space space space space space equals space fraction numerator n squared open parentheses n plus 1 close parentheses squared over denominator 2 end fraction space plus space fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction space space space space space space space space space space space space space equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction open square brackets n open parentheses n plus 1 close parentheses space plus space fraction numerator 2 n plus 1 over denominator 3 end fraction close square brackets space space space space space space space space space space space space space space equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction space open square brackets fraction numerator 3 n squared space plus space 3 n space plus space 2 n plus space 1 over denominator 3 end fraction close square brackets space space space space space space space space space space space space space space equals space fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction space open square brackets fraction numerator 3 n squared space plus space 5 n space plus 1 over denominator space 3 end fraction close square brackets space space space space space space space space space space space space space space space equals fraction numerator n open parentheses n plus 1 close parentheses open parentheses 3 n squared space plus space 5 n space plus 1 close parentheses over denominator 6 end fraction$}

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

< Previous Question

Next Question >

Popular questions of class 11 Mathematics

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Q: Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Q: Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Recently Viewed Questions of Class 11 Mathematics

Find the equation of the circle with centre (–2, 3) and radius 4

A die is thrown. Describe the following events:

(i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3

(iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3

Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F’, F’

Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

Q: Write the following sets in the set-builder form:
(i) (3, 6, 9, 12)
(ii) {2, 4, 8, 16, 32}
(iii) {5, 25, 125, 625}
(iv) {2, 4, 6 upto infinity}
(v) {1, 4, 9, upto 100}

Solve each of the following equations:

x² + 3 = 0

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.

Find the sum to n terms of the sequence, 8, 88, 888, 8888…

Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Sequence and Series.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

Dhanush
2019-11-20 07:04:38

Wow

Comment(s) on this Question

Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 4 , Question 3: Find the sum to n terms of the series 3 × 12 + 5 × 22 + 7 × 32....

Find the sum to n terms of the | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

< Previous Question

Next Question >

Popular questions of class 11 Mathematics

Recently Viewed Questions of Class 11 Mathematics

Study Tips for Answering NCERT Questions:

Comments

Comment(s) on this Question

Chapters for Class 11 Mathematics

Subjects for Class 11

Students Also Read

Important links

Quick Links

Resources

Support