← Back to topic
Vidaara.orgClass 11 · Mathematics
CodeVID-M11-08-GP-01
Geometric Progression & Mean — Assignment
Chapter: Sequences and Series
Topic: Geometric Progression (GP) and Geometric Mean
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The $n$th term of a GP is:
  • A.$a+(n-1)d$
  • B.$ar^{n-1}$
  • C.$ar^n$
  • D.$nr$
2.
The common ratio of $3,6,12,\dots$ is:
  • A.$1$
  • B.$2$
  • C.$3$
  • D.$6$
3.
The geometric mean of $4$ and $9$ is:
  • A.$6$
  • B.$6.5$
  • C.$13$
  • D.$36$
4.
The sum to infinity of a GP with $|r|<1$ is:
  • A.$\tfrac{a}{1-r}$
  • B.$\tfrac{a}{r-1}$
  • C.$a(1-r)$
  • D.$\tfrac{a}{r}$
5.
The $4$th term of $1,2,4,\dots$ is:
  • A.$6$
  • B.$8$
  • C.$16$
  • D.$4$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the $5$th term of the GP $3,6,12,\dots$
7.
Find the common ratio if $a=2$ and $a_4=54$.
8.
Find the geometric mean of $2$ and $8$.
9.
Find the sum to infinity of $1+\tfrac12+\tfrac14+\dots$
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the sum of the first $6$ terms of the GP $2,6,18,\dots$
11.
Which term of the GP $2,4,8,\dots$ is $256$?
12.
Find the sum to infinity of $6-2+\tfrac23-\dots$
13.
Insert two geometric means between $1$ and $27$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The sum of three numbers in GP is $13$ and their product is $27$. Find the numbers.
15.
Find the sum to $n$ terms of $7+77+777+\dots$

Answer Key

Section A — Multiple Choice Questions
  1. (B) $ar^{n-1}$
  2. (B) $2$
  3. (A) $6$
  4. (A) $\tfrac{a}{1-r}$
  5. (B) $8$
Section B — Short Answer (2 marks)
  1. $48$.
  2. $3$.
  3. $4$.
  4. $2$.
Section C — Short Answer (3 marks)
  1. $728$.
  2. The $8$th term.
  3. $\tfrac92$.
  4. $3$ and $9$.
Section D — Long Answer (5 marks)
  1. $1,3,9$.
  2. $\dfrac{7}{81}\left(10^{n+1}-9n-10\right)$.
Generated by Vidaara.org · Assignment VID-M11-08-GP-01 · vidaara.org