Welcome to Part 1 of our new 8-part series on Chapter 5, Arithmetic Progressions (AP). This post contains the top 25 Multiple Choice Questions (MCQs) to help you master the concepts of the nth term, sum of n terms, and common difference.
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Top 25 MCQs - Arithmetic Progressions
Question 1: Identify AP
Which of the following lists of numbers forms an AP?
In (b): 5/2 - 2 = 0.5; 3 - 5/2 = 0.5; 7/2 - 3 = 0.5.
Since 'd' is constant (0.5), it is an AP.
Question 2: Finding n-th Term
The 10th term of the AP: 5, 8, 11, 14, ... is:
aₙ = a + (n-1)d
a₁₀ = 5 + (10-1)3 = 5 + 9(3) = 5 + 27 = 32.
Question 3: Finding d
If the common difference of an AP is 5, then what is a₁₈ - a₁₃?
Given d = 5.
So, 5(5) = 25.
Question 4: First Negative Term
Which term of the AP: 21, 18, 15, ... is zero?
0 = 21 + (n-1)(-3)
3(n-1) = 21 => n-1 = 7 => n = 8.
Question 5: Value of k
If k, 2k-1, and 2k+1 are three consecutive terms of an AP, the value of k is:
2(2k - 1) = k + (2k + 1)
4k - 2 = 3k + 1
k = 3.
Question 6: 30th Term
The 30th term of the AP: 10, 7, 4, ... is:
a₃₀ = 10 + (29)(-3) = 10 - 87 = -77.
Question 7: Sum of First n Integers
The sum of the first n positive integers is given by:
Question 8: Term from End
The 4th term from the end of the AP: -11, -8, -5, ..., 49 is:
New first term (a) = 49. Common difference (d) becomes -3 (opposite of original +3).
a₄ = a + 3d = 49 + 3(-3) = 49 - 9 = 40.
Question 9: Number of Terms
How many two-digit numbers are divisible by 3?
a = 12, d = 3, aₙ = 99.
99 = 12 + (n-1)3 => 87 = 3(n-1) => 29 = n-1 => n = 30.
Question 10: Sum of n Terms
The sum of the first 20 terms of the AP: 1, 4, 7, 10, ... is:
S₂₀ = 20/2 [2(1) + (19)3]
= 10 [2 + 57] = 10 [59] = 590.
Question 11: Common Difference from Sn
If the sum of first n terms of an AP is An² + Bn, then the common difference is:
Question 12: Missing Term
If 18, a, b, -3 are in AP, then a + b = ?
a + b = 18 + (-3) = 15.
Question 13: 11th Term
The 11th term of the AP: -5, -5/2, 0, 5/2, ... is:
a₁₁ = -5 + 10(2.5) = -5 + 25 = 20.
Question 14: First Five Multiples of 3
The sum of the first five multiples of 3 is:
Sum = 3(1+2+3+4+5) = 3(15) = 45.
Question 15: a30 - a20
For an AP with common difference 'd', the value of a₃₀ - a₂₀ is:
a₃₀ - a₂₀ = (a + 29d) - (a + 19d) = 10d.
Question 16: Which Term is 210
Which term of the AP: 21, 42, 63, 84, ... is 210?
210 = 21 + (n-1)21
210 = 21n => n = 10.
Question 17: Middle Term
The middle term of the AP: 6, 13, 20, ..., 216 is:
Since n is odd, middle term is (n+1)/2 = 16th term.
a₁₆ = 6 + 15(7) = 6 + 105 = 111.
Question 18: Sum of Odd Numbers
The sum of the first 20 odd natural numbers is:
Here n = 20. So, Sum = (20)² = 400.
Question 19: First Negative Term
Which term of the AP: 121, 117, 113, ... is its first negative term?
121 + (n-1)(-4) < 0
121 - 4n + 4 < 0
125 < 4n => n > 31.25.
So, n = 32.
Question 20: Value of x
If x+2, 2x, and 2x+3 are in AP, the value of x is:
2(2x) = (x+2) + (2x+3)
4x = 3x + 5
x = 5. Wait, let me recheck.
a=5+2=7, b=10, c=10+3=13. d=3. Correct.
Wait, option (a) says 3. Let's check x=3. a=5, b=6, c=9. d=1, d=3. Not AP.
My calculation says x=5. Let's check options again.
(c) is 5. So correct option is (c).
Correction: The correct option in the code should be (c).
Question 20: Value of x
If x+2, 2x, and 2x+3 are in AP, the value of x is:
4x = 3x + 5
x = 5.
Question 21: 10th Term Calculation
The 10th term of the AP: √2, √8, √18, ... is:
a = √2, d = √2.
a₁₀ = a + 9d = √2 + 9√2 = 10√2.
10√2 = √(100 * 2) = √200.
Question 22: n-th Term Formula
If the nth term of an AP is 5n - 2, find the common difference.
Question 23: Divisible by 4
How many multiples of 4 lie between 10 and 250?
248 = 12 + (n-1)4
236 = 4(n-1) => 59 = n-1 => n = 60.
Question 24: Sum of Positive Integers
The sum of the first 100 positive integers is:
Question 25: Sum of n terms
If the first term is 5, last term is 45, and sum is 400, find the number of terms.
400 = n/2 (5 + 45)
400 = n/2 (50) = 25n
n = 400 / 25 = 16.
