级数 - 在线测验

以下测验提供与级数相关的多项选择题 (MCQ)。您需要阅读所有给出的答案，然后点击正确的答案。如果您不确定答案，可以使用显示答案按钮查看答案。您可以使用下一测验按钮查看测验中的新一组问题。

问题 1 - 等差数列 4, 9/2, 5, 11/2, 6 ....的第 105 项是

答案：A

解释

 Here a = 4, d = (9/2-4) = 1/2
T₁0₅ = a+(105-1)*d=4+104*1/2=4+52=56.

问题 2 - 序列 72+63 + 54+ ....的哪一项为零？

答案：B

解释

Given series is an A.P. in which a=72 and d = (63-72)= -9
Let the nth term be 0. Then a+ (n-1) d =0 ⇒ 72+ (n-1)*(-9) = 0 ⇒ 72-9n +9 =0
⇒ 9n =81 ⇒ n = 9
∴ 9th term is the given series is 0.

问题 3 - 在 100 和 200 之间同时能被 9 和 6 整除的整数的总数是

答案：B

解释

LCM of 9 and 6 = 18
So, each one must be multiple of 18.
Requisite no. is 108,126, 144, 162, 180, 198.
Their no. is 6.

问题 4 - (45+46+47....+113+114+115)?

答案：D

解释

Here a=45, d =1 and L=115.
A+ (n-1) d = 115 ⇒ 45+ (n-1) *1 = 115
(n-1 ) = 70 ⇒ n = 71
Sum = n/2 * (a+L) = 71/2 * (45 +115) = 71/2 *160 = (71 *80) = 5680.

问题 5 - 如果 a, a-2,3a 成等差数列，则 a=？

答案：B

解释

Since a, (a-2), 3a are in A.P. , we have
(a-2) - a = 3a - (a-2) ⇒ 2a +2 = -2 ⇒ 2a = -4 ⇒ a = -2.

问题 6 - 如果一个等比数列的第四项和第九项分别为 54 和 13122，则它的第二项是

答案：A

解释

Let its 1st term be a and common ratio r. Then,
ar³ = 54 and ar⁸ = 13122
∴ ar⁸/ ar³ = 13122/54 ⇒ r⁵ =243 = 3⁵ =r = 3
∴ a* 3³ = 54 ⇒ a*27 = 54 = > a =2
2nd term = ar = (2*3) =6

问题 7 - 和 (1+1/2+1/4+1/8+1/16+..... =?

答案：A

解释

This is an infinite G.P in which a =1 and r = 1/2
Sum of infinite G.P. = a/ (1-r) = 1/ (1-1/2) =2

问题 8 - 一个钟表在 1 点钟响 1 下，2 点钟响 2 下，3 点钟响 3 下，依此类推。一天中钟表的总响声是多少？

答案：C

解释

Total number of buzzes =2 (1+2+3+..........+12).
This is an A.P. in which a=1, d=1, n = 12 and L = 12.
(1+2+3+ .........+12) = 12/2* (1+12) = 78.
∴ Total number of buzzes = (2 * 78) = 156.

问题 9 - (14² +15² +......+30²) =?

答案：D

解释

We know that (1²+2²+3²+... +a²) = {n(n+1)(2n+1)}/6
Given Exp. = (1²+2²+...+13²+14²+??+30²)-(1²+2²+...+13²)
= (30*31*61)/6 - (13*14*27)/6 = (9455- 819) = 8636

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