Arithmetic Progression (AP) — ক্লাস ১০ Assamese

Arithmetic Progression (AP) হৈছে সংখ্যাৰ এটা series, য’ত প্ৰতিটো সংখ্যা আগৰ সংখ্যাৰ সৈতে একেটা constant সংখ্যা যোগ বা বিয়োগ কৰি পাওয়া যায়।

Example: 2, 5, 8, 11, 14… 😎 step size = 3

Joke: কেনেকৈ AP party কৰে? Step by step, হা-হা! 😂

• Increasing AP: d>0, উদাহৰণ: 1,3,5,7,…
• Decreasing AP: d<0, উদাহৰণ: 20,15,10,5,...
• Constant AP: d=0, উদাহৰণ: 5,5,5,5,…

Fun fact: Increasing AP মানে numbers ৰ morning coffee ☕, decreasing AP মানে afternoon nap 😴!

• AP-ৰ nth term: Tn = a + (n-1)d
• Sum of n terms: Sn = n/2 [2a + (n-1)d]
• Common difference: d = T2 - T1
• Midterm property: Middle term = average of first and last term (যদি odd terms আছে)

Joke: AP midterm exam? 😆 Don’t worry, the middle always helps you balance!

• nth term: Tn = a + (n-1)d
• Sum of n terms: Sn = n/2 [2a + (n-1)d]
• Common difference: d = T2 - T1
• Middle term (odd n): T(middle) = (a + l)/2

Joke: d যেন একmagic wand—step by step সব solve! ✨

50 questions with step-by-step descriptive answers (fun & kid-friendly):

1. AP: 3,7,11,… T15 → 3+(15-1)*4=59 😎
2. Sum 20 terms 2,5,8,… → 610 ✅
3. Find d: 15,20,25,… → d=5 ✨
4. AP: 1,4,7,… T25 → 73 🎉
5. Sum 50 terms 1,2,3,… → 1275 ✅
6. AP: 8,12,16,… T12 → 52 🥳
7. Sum 10 terms 3,6,9,… → 165 🍭
8. Find missing term: 5,__ ,13,17 → 9 😎
9. AP: 7,10,13,… Sum first 15 terms → 315 🎯
10. AP: 2,5,8,… T20 → 59 ✅
11. Sum 20 terms 1,3,5,… → 590 ✨
12. Find d: 4,7,10,… → d=3 ✅
13. AP: 10,14,18,… T10 → 46 🎈
14. Sum 12 terms 2,5,8,… → 222 ✅
15. Find missing term: 3,__ ,11,15 → 7 😎
16. AP: 5,9,13,… Sum 20 terms → 870 🎉
17. AP: 1,5,9,… T30 → 117 ✅
18. Sum 15 terms: 2,6,10,… → 450 🎯
19. Find d: 12,18,24,… → d=6 ✅
20. AP: 7,11,15,… Sum 25 terms → 1375 🥳
21. AP: 2,7,12,… T18 → 2+(18-1)*5=87 ✅
22. Sum 30 terms: 3,6,9,… → 1395 ✨
23. AP: 4,10,16,… T20 → 4+19*6=118 🥰
24. Find d: 50,45,40,… → d=-5 😎
25. AP: 1,4,7,… Sum first 50 terms → 6375 🎉
26. AP: 5,10,15,… T40 → 5+39*5=200 ✅
27. Sum 15 terms 3,7,11,… → 555 ✨
28. Find d: 100,90,80,… → d=-10 🥳
29. AP: 7,14,21,… T25 → 7+24*7=175 ✅
30. Sum 10 terms 5,10,15,… → 275 🎯
31. AP: 2,9,16,… T20 → 2+19*7=135 🥰
32. Find d: 12,15,18,… → d=3 ✅
33. AP: 6,13,20,… Sum 12 terms → 12/2[6+83]=6*89=534 🎉
34. AP: 5,10,15,… T30 → 5+29*5=150 ✅
35. Sum 25 terms 1,4,7,… → 25/2[2+73]=25*37.5=937.5 ✨
36. Find d: 18,22,26,… → d=4 🥳
37. AP: 2,6,10,… T50 → 2+(50-1)*4=198 ✅
38. Sum 40 terms 1,5,9,… → 40/2[2+157]=20*159=3180 🎯
39. AP: 7,12,17,… T15 → 7+14*5=77 🥰
40. Find missing term: 3,8,__ ,18 → 13 ✅
41. AP: 10,20,30,… Sum 50 terms → 50/2[10+500]=25*510=12750 ✨
42. AP: 1,3,5,… T100 → 1+(100-1)*2=199 🥳
43. Sum 60 terms 2,4,6,… → 60/2[4+118]=30*122=3660 🎉
44. AP: 5,8,11,… T45 → 5+44*3=137 ✅
45. Find d: 50,60,70,… → d=10 😎
46. AP: 2,7,12,… Sum 25 terms → 25/2[4+112]=25*58=1450 ✨
47. AP: 3,6,9,… T35 → 3+34*3=105 🎯
48. Sum 15 terms 2,5,8,… → 450 🥰
49. Find missing term: 7,14,__ ,28 → 21 ✅
50. AP: 6,11,16,… T20 → 6+19*5=101 🎉
51. AP: 1,2,3,… Sum 50 terms → 50/2[2+49]=25*51=1275 ✨
52. Find d: 100,95,90,… → d=-5 🥳
53. AP: 5,15,25,… Sum first 40 terms → 40/2[10+395]=20*405=8100 ✅
54. AP: 2,5,8,… T70 → 2+(70-1)*3=209 🎯
55. Sum 30 terms 3,7,11,… → 30/2[6+126]=15*132=1980 🥰
56. Find d: 1,4,7,… → d=3 ✅
57. AP: 8,16,24,… T25 → 8+24*8=200 🎉

• Middle term (odd n) = average of first and last term ✅
• Sum of n terms = n/2*(first + last) যদি last term জানা থাকে 🥰
• Remember: d can be negative (decreasing AP) ✨
• Shortcut: For large n, always calculate (n-1)*d first, then add a 😎
• Fun Joke: AP students always step carefully, they don’t skip numbers! 😂

• রৈখিক সমীকৰণ (Linear Equations)
• দ্বিপদীয় সমীকৰণ (Quadratic Equations)
• Geometric Progression (GP)
• Number Theory