Class 11 Math - Sequences and Series - MERIT YARD
Class 11 Math - Sequences & Series - MERIT YARD
1 / 40The general term of a sequence is given by \( a_n = 2n + 1 \).
Find the first term \( a_1 \).
A) \( 3 \)
B) \( 1 \)
C) \( 5 \)
D) \( 2 \)
2 / 40In an AP, if the first term \( a = 5 \) and common difference \( d = 3 \).
Find the second term \( a_2 \).
A) \( 15 \)
B) \( 2 \)
C) \( 8 \)
D) \( 5 \)
3 / 40Find the Geometric Mean (GM) between
the numbers \( 4 \) and \( 9 \).
A) \( 5 \)
B) \( 6 \)
C) \( 13 \)
D) \( 36 \)
4 / 40The sum of the first \( n \) natural numbers is mathematically given by:
A) \( n^2 \)
B) \( \frac{n}{2} \)
C) \( n(n+1) \)
D) \( \frac{n(n+1)}{2} \)
5 / 40If three numbers \( a, b, c \) are in Arithmetic Progression (AP), then:
A) \( b = a + c \)
B) \( 2b = a + c \)
C) \( b^2 = ac \)
D) \( 2a = b + c \)
6 / 40What is the formula for the \( n^{\text{th}} \) term of an Arithmetic Progression (AP)?
A) \( a + (n-1)d \)
B) \( a + nd \)
C) \( ar^{n-1} \)
D) \( a - (n-1)d \)
7 / 40A sequence that contains an endless number of terms is called an:
A) Finite sequence
B) AP series
C) Infinite sequence
D) Empty sequence
8 / 40In a Geometric Progression (GP), if \( a = 3 \) and \( r = 2 \).
Find the second term \( a_2 \).
A) \( 5 \)
B) \( 1 \)
C) \( 9 \)
D) \( 6 \)
9 / 40What is the standard relation between Arithmetic Mean (AM) and Geometric Mean (GM) for two distinct positive numbers?
A) \( \text{AM} < \text{GM} \)
B) \( \text{AM} = \text{GM} \)
C) \( \text{AM} > \text{GM} \)
D) \( \text{AM} \le \text{GM} \)
10 / 40The general term of a sequence is given by \( a_n = n^2 \).
Find the second term \( a_2 \).
A) \( 2 \)
B) \( 4 \)
C) \( 8 \)
D) \( 1 \)
11 / 40The formula for the sum of \( n \) terms of a GP when the common ratio \( r > 1 \) is:
A) \( a\frac{r^n - 1}{r - 1} \)
B) \( a\frac{1 - r^n}{1 - r} \)
C) \( \frac{a}{1 - r} \)
D) \( na \)
12 / 40In an AP, the difference between any two consecutive terms is always:
A) Increasing
B) Decreasing
C) Zero
D) Constant
13 / 40Find the common difference \( d \) of the Arithmetic Progression:
\( 10, 7, 4, \dots \)
A) \( 3 \)
B) \( 17 \)
C) \( -3 \)
D) \( 0 \)
14 / 40The sum of an infinite GP where \( |r| < 1 \) is properly given by the formula:
A) \( \frac{a}{r-1} \)
B) \( \frac{a}{1-r} \)
C) \( a(1-r) \)
D) \( \infty \)
15 / 40The Arithmetic Mean (AM) between any two real numbers \( a \) and \( b \) is:
A) \( \frac{a+b}{2} \)
B) \( \sqrt{ab} \)
C) \( a+b \)
D) \( \frac{a-b}{2} \)
16 / 40What is the \( 10^{\text{th}} \) term of the simple AP:
\( 1, 2, 3, \dots \)?
A) \( 9 \)
B) \( 11 \)
C) \( 20 \)
D) \( 10 \)
17 / 40Find the \( 5^{\text{th}} \) term of the Geometric Progression (GP):
\( 2, 4, 8, \dots \)
A) \( 16 \)
B) \( 64 \)
C) \( 32 \)
D) \( 20 \)
18 / 40A sequence that contains a limited and countable number of terms is called a:
A) Null sequence
B) Finite sequence
C) Infinite sequence
D) Geometric sequence
19 / 40If the first term of an AP is \( a \) and the last term is \( l \), what is the sum \( S_n \)?
A) \( \frac{n}{2}(a + l) \)
B) \( n(a + l) \)
C) \( \frac{n}{2}(a - l) \)
D) \( \frac{a+l}{2} \)
20 / 40The general formula for the sum of \( n \) terms of an AP is:
A) \( \frac{n}{2}[a + (n-1)d] \)
B) \( n[2a + (n-1)d] \)
C) \( a + (n-1)d \)
D) \( \frac{n}{2}[2a + (n-1)d] \)
21 / 40If three non-zero numbers \( a, b, c \) are in Geometric Progression (GP), then:
A) \( b = a + c \)
B) \( b^2 = a + c \)
C) \( b^2 = ac \)
D) \( 2b = ac \)
22 / 40In a GP, if the common ratio \( r \) is a negative number, the consecutive terms will:
A) Become zero
B) Alternate in sign
C) Always be negative
D) Always be positive
23 / 40Find the sum of the infinite GP:
\( 1, \frac{1}{2}, \frac{1}{4}, \dots \)
A) \( 2 \)
B) \( 1.5 \)
C) \( \infty \)
D) \( 1 \)
24 / 40The sequence \( 2, 4, 6, 8, \dots \) is a clear example of an:
A) Harmonic Progression
B) Geometric Progression
C) Infinite Series
D) Arithmetic Progression
25 / 40Find the \( 4^{\text{th}} \) term of the GP where the first term \( a = 1 \) and common ratio \( r = 10 \).
A) \( 40 \)
B) \( 100 \)
C) \( 1000 \)
D) \( 10000 \)
26 / 40The Geometric Mean (GM) between two positive numbers \( a \) and \( b \) is calculated as:
A) \( \frac{ab}{2} \)
B) \( \sqrt{ab} \)
C) \( a^2 + b^2 \)
D) \( \frac{a+b}{2} \)
27 / 40If \( \text{AM} = \text{GM} \) for two positive numbers \( a \) and \( b \), then it strictly implies that:
A) \( a = b \)
B) \( a > b \)
C) \( a < b \)
D) \( a \neq b \)
28 / 40In a GP, the constant number multiplied to a term to get the next term is called the:
A) Common multiple
B) Common difference
C) Constant sum
D) Common ratio
29 / 40Find the Arithmetic Mean (AM) between
the numbers \( 2 \) and \( 8 \).
A) \( 4 \)
B) \( 10 \)
C) \( 6 \)
D) \( 5 \)
30 / 40Find the \( 3^{\text{rd}} \) term of the sequence given by:
\( a_n = (-1)^n \cdot n \)
A) \( 3 \)
B) \( -3 \)
C) \( 1 \)
D) \( -1 \)
31 / 40In an AP, the constant number added to a term to get the next term is known as the:
A) First term
B) Common ratio
C) Common difference
D) Common factor
32 / 40In a GP, if the common ratio \( r = 1 \), what is the sum of the first \( n \) terms?
A) \( na \)
B) \( a^n \)
C) \( 0 \)
D) \( n+a \)
33 / 40The specific sequence \( 1, 4, 9, 16, \dots \) represents the sequence of:
A) Cubes
B) Prime numbers
C) Even numbers
D) Squares
34 / 40Find the common ratio \( r \) of the GP:
\( 5, 15, 45, \dots \)
A) \( 5 \)
B) \( 3 \)
C) \( 10 \)
D) \( 15 \)
35 / 40What is the sum of the first 10 terms of the constant sequence \( 1, 1, 1, \dots \)?
A) \( 1 \)
B) \( 11 \)
C) \( 10 \)
D) \( 0 \)
36 / 40Find the Geometric Mean (GM) between
the numbers \( 2 \) and \( 8 \).
A) \( 4 \)
B) \( 16 \)
C) \( 5 \)
D) \( 10 \)
37 / 40Find the common ratio \( r \) for the alternating GP:
\( 1, -1, 1, -1, \dots \)
A) \( 1 \)
B) \( 0 \)
C) \( 2 \)
D) \( -1 \)
38 / 40What is the formula for the \( n^{\text{th}} \) term of a Geometric Progression (GP)?
A) \( ar^n \)
B) \( ar^{n-1} \)
C) \( (ar)^{n-1} \)
D) \( a + r^n \)
39 / 40What is the Arithmetic Mean (AM) between
the numbers \( 4 \) and \( 9 \)?
A) \( 6 \)
B) \( 13 \)
C) \( 6.5 \)
D) \( 5 \)
40 / 40The sequence \( 3, 9, 27, 81, \dots \) is a clear example of a:
A) Geometric Progression
B) Arithmetic Progression
C) Harmonic Progression
D) Fibonacci Sequence
Test Analysis

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Wrong ❌ 0

Unattempted ⚠️ 40

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Time Taken ⏱️ 00m 00s

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