Progressiyalar (arifmetik va geometrik) — test savollari javoblari bilan
Matematika · 5 ta ochiq savol (bankda jami 11 ta) · har birida to'g'ri javob va izoh
1. $1^3 + 2^3 + 3^3 + ... + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ formuladan $1^3 + 2^3 + ... + 10^3$ ni toping.
- A) $3025$
- B) $2025$
- C) $4025$
- D) $5025$
Javobni ko'rish
To'g'ri javob: A) $3025$
2. $\sum_{k=0}^{\infty} \left(\frac{1}{2}\right)^k = ?$ (geometrik progressiya yig'indisi)
- A) $1$
- B) $2$
- C) $\infty$
- D) $\frac{1}{2}$
Javobni ko'rish
To'g'ri javob: B) $2$
3. $\frac{x - 1}{3} = \frac{y + 2}{5}$ va $x + y = 14$ bo'lsa, $x$ ni toping.
- A) $4$
- B) $5$
- C) $7$
- D) $6$
Javobni ko'rish
To'g'ri javob: C) $7$
4. $a$, $b$, $c$ arifmetik progressiyada, $a$, $d$, $b$ geometrik progressiyada, $b$, $e$, $c$ garmonik progressiyada. Agar $a = 1$, $c = 9$ bo'lsa, $d \cdot e$ ni toping.
- A) $15$
- B) $\frac{45}{2}$
- C) $\frac{90}{7}$
- D) $18$
Javobni ko'rish
To'g'ri javob: C) $\frac{90}{7}$
5. $\sin^2 2x - \sin^2 x = \cos^2 x$ tenglamaning $[0; 2\pi)$ da nechta ildizi bor?
- A) $2$
- B) $4$
- C) $6$
- D) $8$
Javobni ko'rish
To'g'ri javob: B) $4$
Bu — mavzuning ochiq namuna qismi. To'liq bank, vaqt rejimi, tahlil va xatolar ustida ishlash — test rejimida.