413. Agar arifmetik progressiyada:

   l) a =1, a_n = 20, n = 50;

3) a₁=-1, a_n = -40, n = 20;

2) a₁ =1, a_n = 200, n = 100;

4) a₁ = 2, a_n = 100, n = 50 bo'lsa, uning dastlabki n ta hadining yig'indisini toping.

414.      2 dan 98 gacha bo'lgan barcha natural sonlar yig'indisini toping (98 ham yig'indiga kiradi).

415.      1 dan 133 gacha bo'lgan barcha toq sonlarning yig'indisini toping (133 ham yig'indiga         kiradi).

416. Agar arifmetik progressiyada:  l) a₁ = -5, d = 0,5; 2)a₁=,d = -3 bo'lsa, uning dastlabki o'n ikkita hadi yig'indisini toping.

417. 1) agar n =11 bo'lsa, 9;   13;   17;...; 2) agar n = 12 bo'lsa, -16;   -10;   -4;... arifmetik progressiyaning dastlabki n ta hadi yig'indisini toping.

418. Agar:  1) 3 + 6 + 9 + ... + 273; 2) 90 + 80 + 70 + ... + (-60) yig'indining qo'shiluvchilari arifmetik progressiyaning ketma-ket hadlari bo'lsa, shu         yig'indini toping.

419. Barcha ikki xonali, barcha uch xonali sonlar yig'indisini toping.

420. Arifmetik progressiya n- hadining formulasi bilan berilgan. Agar:  1) a_n = 3n + 5; 2) a_n = 7 + 2n bo'lsa, S₅₀ ni toping.

421. Yig'indi 75 ga teng bo'lishi uchun 3 dan boshlab nechta ketma-ket natural sonni qo'shish         kerak?

422. Agar arifmetik progressiyada: 1) a₁ = 10, n=14,   S₁₄=1050; 2) a₁=2,  n=10,   S₁₀=90 bo'lsa, a_n va d ni toping.

423. Agar arifmetik progressiyada:  l) a₇ = 21,   S₇ = 205; 2) a₁₁ = 92,  S₁₁ = 22 bo'lsa, a₁ va d ni toping.

424. Binobop to'sinlarni saqlashda ularni 75- rasmda ko'rsatilgandek taxlaydilar. Agar   taxlamning asosida 12 ta to'sin turgan bo'lsa, bir taxlamda nechta to'sin bo'ladi?

425. Arifmetik progressiyada a₃ + a₉ = 8. S₁₁ ni toping.

426. Agar arifmetik progressiyada S₅ = 65 va S₁₀ = 230 bo'lsa, uning birinchi hadini va  ayirmasini toping. Arifmetik progressiya uchun S₁₂ = 3(S₈ – S₄) tenglik bajarilishini isbotlang.

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