Free · Class 10 · 6 worksheets · answer keys · practise online · set 51
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 51
Name: Date: Score: / 10
Find d.
Common difference of 4, 0, −4, −8, … Common difference of 17, 28, 39, 50, … Common difference of −13, −19, −25, −31, … Common difference of 20, 8, −4, −16, … Common difference of −10, −8, −6, −4, … Common difference of 20, 22, 24, 26, … Common difference of −14, −22, −30, −38, … Common difference of 15, 14, 13, 12, … Common difference of 14, 24, 34, 44, … Common difference of −10, −16, −22, −28, …
✅ Answer key — Common difference
d = −4 d = 11 d = −6 d = −12 d = 2 d = 2 d = −8 d = −1 d = 10 d = −6 TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Is it an AP? Class 10 · Worksheet 2 · set 51
Name: Date: Score: / 8
Answer, and give d if it is an AP.
Is 7, 12, 14, 22 an AP? Is 5, −1, −6, −13 an AP? Is 7, −1, −9, −17 an AP? Is 3, −5, −9, −15 an AP? Is 15, 6, −3, −12 an AP? Is −8, −4, 0, 2 an AP? Is 18, 23, 29, 33 an AP? Is 1, −3, −10, −11 an AP?
✅ Answer key — Is it an AP?
No No Yes, d = −8 No Yes, d = −9 No No No TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
nth term Class 10 · Worksheet 3 · set 51
Name: Date: Score: / 8
Find the term.
The 25th term of −15, −24, −33, … The 27th term of 15, 6, −3, … The 21st term of −1, −9, −17, … The 21st term of −7, −11, −15, … The 24th term of 9, 17, 25, … The 22nd term of −19, −12, −5, … The 35th term of −19, −11, −3, … The 25th term of −17, −8, 1, …
✅ Answer key — nth term
−231 −219 −161 −87 193 128 253 199 TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Which term? Class 10 · Worksheet 4 · set 51
Name: Date: Score: / 8
Solve.
Which term of −17, −24, −31, … is −241? Which term of 15, 23, 31, … is 303? Which term of −20, −14, −8, … is 94? Which term of −10, −13, −16, … is −88? Which term of −8, −17, −26, … is −323? Which term of 1, −8, −17, … is −134? Which term of 6, 11, 16, … is 101? Which term of 12, 6, 0, … is −204?
✅ Answer key — Which term?
the 33rd term the 37th term the 20th term the 27th term the 36th term the 16th term the 20th term the 37th term TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Sum of n terms Class 10 · Worksheet 5 · set 51
Name: Date: Score: / 8
Find the sum.
Sum of the first 16 terms of 13, 18, 23, … Sum of the first 15 terms of −8, −7, −6, … Sum of the first 25 terms of 18, 24, 30, … Sum of the first 23 terms of 8, 9, 10, … Sum of the first 14 terms of −2, 2, 6, … Sum of the first 28 terms of 12, 16, 20, … Sum of the first 28 terms of 14, 9, 4, … Sum of the first 19 terms of 2, −3, −8, …
✅ Answer key — Sum of n terms
808 −15 2250 437 336 1848 −1498 −817 TalentJR · talentjr.in/arithmetic-progression-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
AP word problems Class 10 · Worksheet 6 · set 51
Name: Date: Score: / 6
Solve.
Aman saves ₹400 in the first month and ₹70 more every month after that. How much does he save in 6 months? A hall has 25 seats in the first row and 3 more seats in each row than the row before. How many seats are in the 25th row? Aman saves ₹300 in the first month and ₹20 more every month after that. How much does he save in 8 months? A hall has 11 seats in the first row and 4 more seats in each row than the row before. How many seats are in the 21st row? Aman saves ₹400 in the first month and ₹20 more every month after that. How much does he save in 12 months? Find the sum of all two-digit numbers that are multiples of 6.
✅ Answer key — AP word problems
₹3450 97 ₹2960 91 ₹6120 810 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.
