मराठी

Let < an > Be a Sequence. Write the First Five Term in the Following: A1 = A2 = 2, an = an − 1 − 1, N > 2

Advertisements
Advertisements

प्रश्न

Let < an > be a sequence. Write the first five term in the following:

a1 = a2 = 2, an = a− 1 − 1, n > 2

Advertisements

उत्तर

a1 = a2 = 2, an = a− 1 − 1, n > 2

\[a_3 = a_2 - 1 = 2 - 1 = 1\]

\[ a_4 = a_3 - 1 = 1 - 1 = 0\]

\[ a_5 = a_4 - 1 = 0 - 1 = - 1\]

Hence, the five terms are 2, 2, 1, 0 and \[-\]1 .

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 19: Arithmetic Progression - Exercise 19.1 [पृष्ठ ४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 19 Arithmetic Progression
Exercise 19.1 | Q 4.3 | पृष्ठ ४

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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


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


Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)


A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?


Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

−1, 1/4, 3/2, 11/4, ...


Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.

\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]


Find: 

18th term of the A.P.

\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2},\]


Is 302 a term of the A.P. 3, 8, 13, ...?


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


Find the 12th term from the following arithmetic progression:

 3, 5, 7, 9, ... 201


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.


The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.


Find the sum of the following arithmetic progression :

3, 9/2, 6, 15/2, ... to 25 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.


Find the sum of all integers between 84 and 719, which are multiples of 5.


Find the sum of all integers between 50 and 500 which are divisible by 7.


If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.


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

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


If a, b, c is in A.P., prove that:

a2 + c2 + 4ac = 2 (ab + bc + ca)


If a, b, c is in A.P., prove that:

 a3 + c3 + 6abc = 8b3.


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.


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


A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?


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. whose nth term is xn + y.


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


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


In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is


Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =


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


Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively. 


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


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


Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.


If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.


If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.


The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×