English

If the Sum of N Terms of an A.P. Be 3 N2 − N and Its Common Difference is 6, Then Its First Term is - Mathematics

Advertisements
Advertisements

Question

If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is

Options

  • 2

  • 3

  • 1

  • 4

MCQ

Solution

2

\[S_n = 3 n^2 - n\]

\[ \Rightarrow S_1 = 3 \left( 1 \right)^2 - 1\]

\[ \Rightarrow S_1 = 2\]

\[ \therefore a_1 = 2\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 19: Arithmetic Progression - Exercise 19.9 [Page 51]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 19 Arithmetic Progression
Exercise 19.9 | Q 3 | Page 51

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


How many terms of the A.P.  -6 , `-11/2` , -5... are needed to give the sum –25?


Find the sum to n terms of the A.P., whose kth term is 5k + 1.


If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.


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


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


Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?


A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.


If the sequence < an > is an A.P., show that am +n +am − n = 2am.


Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?


The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.


Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.


An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.


The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.


\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]

\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]


The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.


Find the sum of the following arithmetic progression :

a + b, a − b, a − 3b, ... to 22 terms


Find the sum of the following arithmetic progression :

\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.


Solve: 

25 + 22 + 19 + 16 + ... + x = 115


If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?


If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms?


If the sum of a certain number of terms of the AP 25, 22, 19, ... is 116. Find the last term.


In an A.P. the first term is 2 and the sum of the first five terms is one fourth of the next five terms. Show that 20th term is −112.


If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).


If a, b, c is in A.P., then show that:

 a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.


If a, b, c is in A.P., prove that:

 (a − c)2 = 4 (a − b) (b − c)


A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?


A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job? 


A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?


Write the common difference of an A.P. the sum of whose first n terms is

\[\frac{p}{2} n^2 + Qn\].

If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.


If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be


In the arithmetic progression whose common difference is non-zero, the sum of first 3 n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2 n terms to the next 2 nterms is


Mark the correct alternative in the following question:
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is


Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.


If a1, a2, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ...+ cosec an–1 cosec an) is equal to cot a1 – cot an 


If the sum of n terms of a sequence is quadratic expression then it always represents an A.P


If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×