MIXED QUESTIONS ON ARITHMETIC AND GEOMETRIC PROGRESSION

(1)  Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them.

(i)  1/2n+1

(ii)  (n + 1)(n + 2) / (n + 3)(n + 4)

(iii) 4 (1/2)n

(iv) (−1)n/n

(v) (2n+3) / (3n+4)

(vi) 2018

(vii) (3n−2)/(3n−1)    Solution

(2)  Write the first 6 terms of the sequences whose nth term an is given below.

(i) an = n + 1 if n is odd

            n if n is even               Solution

(ii) an = 1 if n = 1

        2 if n = 2

an−1 + an−2 if n > 2             Solution

(iii)  an =  n if n is 1, 2 or 3

         an−1 + an−2 + an−3 if n > 3                Solution

(3)  Write the nth term of the following sequences.

(i)  2, 2, 4, 4, 6, 6, ................         Solution

(ii)  1/2 , 2/3 , 3/4 , 4/5 , 5/6, ...        Solution

(iii)  1/2 , 3/4 , 5/6 , 7/8 , 9/10, ...        Solution

(iv)  6, 10, 4, 12, 2, 14, 0, 16, −2, . .        Solution

(4) The product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP.          Solution

(5)  Write the nth term of the sequence

3/1222, 5/2232, 7/3242 , . . . as a difference of two terms.      Solution

(6)  If tk is the kth term of a GP, then show that tn−k, tn, tn+kalso form a GP for any positive integer k.    Solution

(7)  If a, b, c are in geometric progression, and if a1/x = b1/y = c1/z, then prove that x, y, z are in arithmetic progression.                Solution

(8)  The AM of two numbers exceeds their GM by 10 and HM by 16. Find the numbers.         Solution

(9)  If the roots of the equation (q − r)x2 + (r − p)x + p − q = 0 are equal, then show that p, q and r are in AP.   Solution

(10)  If a, b, c are respectively the pth, qth and rth terms of a GP, show that (q − r) log a + (r − p) log b + (p − q) log c = 0.   Solution

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. SAT Math Resources (Videos, Concepts, Worksheets and More)

    Dec 23, 24 03:47 AM

    SAT Math Resources (Videos, Concepts, Worksheets and More)

    Read More

  2. Digital SAT Math Problems and Solutions (Part - 91)

    Dec 23, 24 03:40 AM

    Digital SAT Math Problems and Solutions (Part - 91)

    Read More

  3. Digital SAT Math Problems and Solutions (Part - 90)

    Dec 21, 24 02:19 AM

    Digital SAT Math Problems and Solutions (Part - 90)

    Read More