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Bihar Board Class 10 (BSEB) Arithmetic Progressions — practice questions

Explore 32 free Arithmetic Progressions questions in Bihar Board Class 10 (BSEB) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Arithmetic Progressions questions and exercises with answers

Showing questions 1–30 of 32.

In an arithmetic progression, the nth term is given by:Read the answer and worked solution →In an AP, the common difference d is found as:Read the answer and worked solution →The sum of the first n terms of an AP is:Read the answer and worked solution →If the last term is l, the sum of the first n terms of an AP is:Read the answer and worked solution →The common difference of the AP 2, 5, 8, 11, … is:Read the answer and worked solution →The 10th term of the AP 2, 7, 12, … is:Read the answer and worked solution →The common difference of the AP 3, 1, −1, −3, … is:Read the answer and worked solution →Which of the following sequences is an arithmetic progression?Read the answer and worked solution →If the first term of an AP is 5 and the common difference is 3, its 4th term is:Read the answer and worked solution →The sum of the first 10 natural numbers (1, 2, 3, …, 10) is:Read the answer and worked solution →The sum of the first n positive integers is given by:Read the answer and worked solution →If the nth term of an AP is $a_n = 3n + 2$, its common difference is:Read the answer and worked solution →How many two-digit numbers are divisible by 3 (i.e. the AP 12, 15, …, 99)?Read the answer and worked solution →Which of the following is an AP?Read the answer and worked solution →Find the common difference of the AP 7, 11, 15, 19, …Read the answer and worked solution →For the AP 12, 9, 6, 3, …, what is d?Read the answer and worked solution →Is 1, 1, 1, 1, … an AP? If yes, what is d?Read the answer and worked solution →Which of these is NOT an AP?Read the answer and worked solution →Find the 20th term of the AP 3, 8, 13, …Read the answer and worked solution →In an AP, a = 7 and d = −2. Find a₁₂.Read the answer and worked solution →The 4th term of an AP is 11 and the 10th term is 29. Find a and d.Read the answer and worked solution →How many terms are there in the AP 7, 13, 19, …, 205?Read the answer and worked solution →Is 150 a term of the AP 11, 8, 5, …?Read the answer and worked solution →Find n if the nth term of the AP −1, 3, 7, … is 95.Read the answer and worked solution →Find the sum of the first 20 terms of the AP 5, 9, 13, …Read the answer and worked solution →Sum the first 15 terms of the AP 3, 7, 11, …Read the answer and worked solution →Sum the AP 2 + 4 + 6 + … + 100.Read the answer and worked solution →How many terms of the AP 3, 6, 9, … add up to 84?Read the answer and worked solution →The sum of first n terms of an AP is Sₙ = 3n² + 5n. Find the 4th term a₄.Read the answer and worked solution →How many three-digit numbers are divisible by 7?Read the answer and worked solution →

Worked practice questions

In an arithmetic progression, the nth term is given by:

$a_n = an + d$
$a_n = a + (n-1)d$
$a_n = a + (n+1)d$
$a_n = a + nd$

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Correct answer: B. $a_n = a + (n-1)d$

nth term: aₙ = a + (n−1)d, where a is the first term, d the common difference.

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In an AP, the common difference d is found as:

$d = a_{n-1} - a_n + 1$
$d = a_n - a_{n-1}$
$d = a_n + a_{n-1}$
$d = a_n \times a_{n-1}$

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Correct answer: B. $d = a_n - a_{n-1}$

Common difference is the gap between consecutive terms: d = aₙ − aₙ₋₁.

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The sum of the first n terms of an AP is:

$S_n = \dfrac{n}{2}[2a + (n-1)d]$
$S_n = \dfrac{n}{2}[a + (n-1)d]$
$S_n = \dfrac{n}{2}[2a + nd]$
$S_n = n[2a + (n-1)d]$

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Correct answer: A. $S_n = \dfrac{n}{2}[2a + (n-1)d]$

Sₙ = n/2 [2a + (n−1)d].

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