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
Advertisements

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

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.


In an A.P., if pth term is 1/q and qth term is 1/p,  prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`


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


The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.


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


If the nth term an of a sequence is given by an = n2 − n + 1, write down its first five terms.


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


Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?


The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.


The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.


If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.


How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?


Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.


Find the sum of the following arithmetic progression :

50, 46, 42, ... to 10 terms


Find the sum of the following serie:

(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]


Solve: 

1 + 4 + 7 + 10 + ... + x = 590.


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


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


If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:

\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.


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

b + c − a, c + a − b, a + b − c are in A.P.


If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that abc are in A.P.


A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.


A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the total product in 7 years and (iii) the product in the 10th year.


There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.


A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?


Write the sum of first n even natural numbers.


Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.


The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be


Mark the correct alternative in the following question:

Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to


The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is 


If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad


The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`


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


A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month


If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.


If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is ______.


Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.


The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×