Questions

1. Question 1

   Find the 6th term of the G.P.: $-6,\ -3,\ -\dfrac{3}{2},\ \ldots$.

   SolutionTheory
2. Question 2

   Find the 8th term of the sequence, $3,\ 3^2,\ 3^3,\ \ldots$.

   SolutionTheory
3. Question 3

   The $n^{th}$ terms of the sequences $1,\ 2,\ 4,\ 8,\ \ldots$ and $256,\ 128,\ 64,\ \ldots$ are equal. Find the value of $n$.

   SolutionTheory
4. Question 4

   Find the first five terms of each sequence described:

   (i)

   $a_1 = 243,\ r = \dfrac{1}{3}$

   (ii)

   $a_1 = 579,\ r = -\dfrac{1}{2}$

   SolutionTheory
5. Question 5

   Find the 12th term of $1 + i,\ 2i,\ -2 + 2i,\ \ldots$.

   SolutionTheory
6. Question 6

   If the 4th and 9th terms of a G.P. are 54 and 13122 respectively. Find the G.P. Also find its general term.

   SolutionTheory
7. Question 7

   If $a,\ b,\ c,\ d$ are in G.P., prove that:

   (i)

   $a - b,\ b - c,\ c - d$ are in G.P.

   (ii)

   $a^2 - b^2,\ b^2 - c^2,\ c^2 - d^2$ are in G.P.

   (iii)

   $a^2 + b^2,\ b^2 + c^2,\ c^2 + d^2$ are in G.P.

   SolutionTheory
8. Question 8

   If $(p+q)^{th}$ term of a G.P. is $m$ and $(p-q)^{th}$ term is $n$, then find the $p^{th}$ term.

   SolutionTheory
9. Question 9

   Find three consecutive numbers in G.P. whose sum is 26 and their product is 216.

   SolutionTheory
10. Question 10

    The 3rd term of a G.P. is the square of 1st term. If the 2nd term is 9 then find the 6th term.

    SolutionTheory
11. Question 11

    If $\dfrac{1}{a},\ \dfrac{1}{b},\ \dfrac{1}{c}$ are in G.P. Show that the common ratio is $\pm\sqrt{\dfrac{a}{c}}$.

    SolutionTheory
12. Question 12

    If the numbers 1, 4 and 3 are subtracted from three consecutive terms of an A.P., the resulting numbers are in G.P. Find the original numbers if their sum is 21.

    SolutionTheory
13. Question 13

    If three consecutive numbers in A.P. are increased by 1, 4, 15 respectively, the resulting numbers are in G.P. Find the original numbers if their sum is 6.

    SolutionTheory
14. Question 14

    If $p^{th},\ q^{th}$ terms of a G.P. are $q$ and $p$ respectively, show that $(p+q)^{th}$ term is $(q^p \cdot p^q)^{\dfrac{1}{p-q}}$.

    SolutionTheory
15. Question 15

    If $a,\ 2a+2,\ 3a+3,\ \ldots$ are in G.P., then find the fifth term.

    SolutionTheory