If the sum of the first m terms of the arithmetic sequence {an} is 30 and the sum of the first 2m terms is 100, then the sum of the first 3M terms of the arithmetic sequence {an} is 30______ ．

If the sum of the first m terms of the arithmetic sequence {an} is 30 and the sum of the first 2m terms is 100, then the sum of the first 3M terms of the arithmetic sequence {an} is 30______ ．

The sum of every m term of the arithmetic sequence {an} is the arithmetic sequence. If the sum of the first 3M term is x, then 30100-30 and X-100 are the arithmetic sequence, so 2 × 70 = 30 + (X-100), x = 210, so the answer is: 210

If the sum of the first m terms of the arithmetic sequence {an} is 30 and the sum of the first 2m terms is 100, then the sum of the first 3M terms of the arithmetic sequence {an} is 30______ ．

The sum of every m term of the arithmetic sequence {an} is the arithmetic sequence. If the sum of the first 3M term is x, then 30100-30 and X-100 are the arithmetic sequence, so 2 × 70 = 30 + (X-100), x = 210, so the answer is: 210

If the sum of the first m terms of the arithmetic sequence {an} is 30 and the sum of the first 2m terms is 100, then the sum of the first 3M terms of the arithmetic sequence {an} is ()
A. 130B. 170C. 210D. 260

Solution 1: let the first term of the arithmetic sequence {an} be A1, and the tolerance be d. from the meaning of the problem, the equation system MA1 + m (m − 1) 2D = 302ma1 + 2m (2m − 1) 2D = 100 is obtained, and the solution is d = 40m2, A1 = 10 (M + 2) m2, ｜ S3M = 3ma1 + 3M & nbsp; (3m − 1) 2D = 3m10 (M + 2) M2 + 3M (3m − 1) 2 × 40m2 = 210. So we choose C. solution 2: ∵ let {an} be the arithmetic sequence, ∵ SM, S2M SM, s3m-s2m be the arithmetic sequence, that is, 30, 70, s3m-100 be the arithmetic sequence, ∵ 30 + s3m-100 = 70 × 2, we get S3M = 210

If the sum of the first m terms of the arithmetic sequence {an} is 30 and the sum of the first 2m terms is 100, then the sum of the first 3M terms of the arithmetic sequence {an} is 30______ ．

The sum of every m term of the arithmetic sequence {an} is the arithmetic sequence. If the sum of the first 3M term is x, then 30100-30 and X-100 are the arithmetic sequence, so 2 × 70 = 30 + (X-100), x = 210, so the answer is: 210

If the sum of the first m terms of the arithmetic sequence {an} is 30 and the sum of the first 2m terms is 100, then the sum of the first 3M terms of the arithmetic sequence {an} is 30______ ．

The sum of every m term of the arithmetic sequence {an} is the arithmetic sequence. If the sum of the first 3M term is x, then 30100-30 and X-100 are the arithmetic sequence, so 2 × 70 = 30 + (X-100), x = 210, so the answer is: 210

Given y = root (2x-5) + root (5-2x + 5), find the arithmetic square root of 2XY

∵ y = radical (2x-5) + radical (5-2x + 5)
∴2x-5＞＝0 5-2x＋5＞＝0
Then: 2.5 ≤ x ≤ 2.5
∴x＝2.5 ∴y＝5
The root sign 2XY = the root sign (2 × 2.5 × 5)
= root 25
＝5
Not necessarily,

If the function y = 1 + 2x + 4xa holds for Y > 0 on X ∈ (- ∞, 1], then the value range of a is______ ．

From the meaning of the question, we get that 1 + 2x + 4xa ＞ 0 is constant on X ∈ (- ∞, 1]; a ＞ - 1 + 2x4x is constant on X ∈ (- ∞, 1]; and ∵ t = - 1 + 2x4x = - (12) 2x - (12) x = - [(12) x + 12] 2 + 14. When x ∈ (- ∞, 1], the range of T is (- ∞, - 34], ｜ a ＞ - 34; that is to say, the range of a is (- 34, + ∞); so the answer is: (- 34, + ∞)

If the function f (x) = 1 + log (A-1) x is a decreasing function in the interval (0, + ∞), then the value range of a is

Here A-1 is the base
Let f (x) = 1 + log (A-1) X
In the interval (0, + ∞), it is a decreasing function,
Should be 0

Given the function f (x) = the logarithm of X with a as the base, (a > O, a is not equal to 1). If f (2a) > - 1, find the value range of real number a

f(2a)=loga 2a>-1
loga 2a +1>0
loga 2a+ loga a>0
loga (2a*a)>0
When a > 1, 2A * a > 1
a^2>1/2
a> √ 2 / 2 or A1
When 0

Take a as the base, the logarithm of 2 is greater than 0 but less than 1, and a is greater than 0 but not equal to 1 to calculate the value range of A

0