Free · Class 10 · 6 worksheets · answer keys · practise online · set 21
Arithmetic progression (AP) worksheets — Class 10
Free arithmetic progression worksheets for Class 10: common difference, nth term, which term, sum of n terms, is it an AP and word problems — with answers.
💡 Learn it first
An AP adds the same number each time: 3, 7, 11, 15… The common difference d = a₂ − a₁ = 4. nth term : aₙ = a + (n − 1)d. Example: the 10th term of 3, 7, 11… is 3 + 9 × 4 = 39.Sum of n terms : Sₙ = n/2 [2a + (n − 1)d] = n/2 (first term + last term).
Common difference (Class 10) Is it an AP? (Class 10) nth term (Class 10) Which term? (Class 10) Sum of n terms (Class 10) AP word problems (Class 10)
Common difference Class 10 · Worksheet 1 · set 21
Name: Date: Score: / 10
Find d.
Common difference of −19, −20, −21, −22, … Common difference of 6, 9, 12, 15, … Common difference of 17, 29, 41, 53, … Common difference of 6, 0, −6, −12, … Common difference of 11, 21, 31, 41, … Common difference of −13, −4, 5, 14, … Common difference of 2, −6, −14, −22, … Common difference of −2, −14, −26, −38, … Common difference of 17, 11, 5, −1, … Common difference of −3, −14, −25, −36, …
✅ Answer key — Common difference
d = −1 d = 3 d = 12 d = −6 d = 10 d = 9 d = −8 d = −12 d = −6 d = −11 TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Is it an AP? Class 10 · Worksheet 2 · set 21
Name: Date: Score: / 8
Answer, and give d if it is an AP.
Is 10, 6, −2, −8 an AP? Is 17, 14, 11, 8 an AP? Is 8, 10, 12, 14 an AP? Is 16, 19, 24, 28 an AP? Is 9, 1, −5, −15 an AP? Is 7, 11, 17, 22 an AP? Is −2, 5, 12, 19 an AP? Is 1, 7, 13, 21 an AP?
✅ Answer key — Is it an AP?
No Yes, d = −3 Yes, d = 2 No No No Yes, d = 7 No TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
nth term Class 10 · Worksheet 3 · set 21
Name: Date: Score: / 8
Find the term.
The 12th term of −16, −15, −14, … The 24th term of −20, −24, −28, … The 36th term of −9, −4, 1, … The 21st term of −4, 3, 10, … The 40th term of 2, −7, −16, … The 35th term of −9, −8, −7, … The 21st term of 4, −3, −10, … The 14th term of −19, −13, −7, …
✅ Answer key — nth term
−5 −112 166 136 −349 25 −136 59 TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Which term? Class 10 · Worksheet 4 · set 21
Name: Date: Score: / 8
Solve.
Which term of 2, 7, 12, … is 87? Which term of −15, −24, −33, … is −357? Which term of −16, −12, −8, … is 172? Which term of −19, −14, −9, … is 171? Which term of −14, −23, −32, … is −320? Which term of −1, −3, −5, … is −61? Which term of 10, 6, 2, … is −106? Which term of 9, 4, −1, … is −31?
✅ Answer key — Which term?
the 18th term the 39th term the 48th term the 39th term the 35th term the 31st term the 30th term the 9th term TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Sum of n terms Class 10 · Worksheet 5 · set 21
Name: Date: Score: / 8
Find the sum.
Sum of the first 20 terms of −7, −8, −9, … Sum of the first 24 terms of 3, −1, −5, … Sum of the first 17 terms of 20, 25, 30, … Sum of the first 20 terms of 20, 28, 36, … Sum of the first 17 terms of 3, 6, 9, … Sum of the first 25 terms of −5, 1, 7, … Sum of the first 9 terms of −9, −11, −13, … Sum of the first 21 terms of 2, 0, −2, …
✅ Answer key — Sum of n terms
−330 −1032 1020 1920 459 1675 −153 −378 TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
AP word problems Class 10 · Worksheet 6 · set 21
Name: Date: Score: / 6
Solve.
Find the sum of all two-digit numbers that are multiples of 3. A hall has 20 seats in the first row and 2 more seats in each row than the row before. How many seats are in the 16th row? Find the sum of all two-digit numbers that are multiples of 8. Find the sum of all two-digit numbers that are multiples of 9. A hall has 18 seats in the first row and 4 more seats in each row than the row before. How many seats are in the 19th row? A hall has 26 seats in the first row and 3 more seats in each row than the row before. How many seats are in the 14th row?
✅ Answer key — AP word problems
1665 50 616 585 90 65 TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Questions
What is the formula for the nth term of an AP? aₙ = a + (n − 1)d, where a is the first term and d the common difference.
Are these worksheets free? Yes — print them or save as PDF free. Every worksheet has an answer key.
How do I get different questions? Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).
How do I print only one worksheet? Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.
Can my child do this worksheet online, like a quiz? Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.
