It is known that the general term formula of the first n terms of the arithmetic sequence {an} is Sn, and a1 + a3 = 10, S4 = 24 (1) to find the general term formula of the sequence {an}

It is known that the general term formula of the first n terms of the arithmetic sequence {an} is Sn, and a1 + a3 = 10, S4 = 24 (1) to find the general term formula of the sequence {an}

A2 = (a1 + a3) / 2 = 5, that is, a1 + D = 5
From S4 = 2 (a1 + A4) = 24, a1 + A4 = 12, that is, 2A1 + 3D = 12
The solution is A1 = 3, d = 2
So an = a1 + (n-1) d = 2n + 1

It is known that the sequence {an} is an arithmetic sequence, Sn is the sum of its first n terms, and a1 + a3 + A5 = 6, S4 = 12. (1) find the general term formula an of the sequence {an}; (2) in the sequence {ANSN}, from which term (including this term) are all positive integers?

(1) The sequence {an} is an arithmetic sequence, and the a1 + a3 + A5 = 6, S4 = 12, and the a1 + a3 + a3 + A5 = 6, S4 = 12, and the a1 + a3 + a3 + A5 = 6, S4 = 12, and the a1 + a3 + a3 + A5 = 6, S4 = 12, and the {a1 + a3 + a3 + a3 + A5 = 6, S4 = 12, and the {a1 + a3 + a3 + A5 = 6, S4 = 12, and the {a1 + A1 + A1 + A1 + A1 + A1 + 2D + 2D + A1 + A1 + 2D + A1 + A1 + A1 + 2D + A1 + A1 + 4D + 4D = 64a1 + 64a1 + 4, A1 = 64a1 + 4, a1 + 4, a1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + A1 + 2D + 2D + 2D + 2D + 2D + 2D + 2D + 2D + 2D + 2D + A1 + 2D + 2D + 2D so when n ≥ 8, an Sn > 0. Therefore, in the sequence {ANSN}, all items starting from the 8th item (including this item) are positive integers

The known sequence an is an arithmetic sequence, the sum of the first n terms is Sn, A3 = - 13, S9 = - 45, (1) find the general formula of the sequence {an}, (2) find the absolute value of the sequence {an}
And T10

(1)S9=9a5=-45
a5=-5
d=(a5-a3)/(5-3)=4
an=4n-25
(2)a6=-1,a7=3,a10=15
S6=(-21-1)×6/2=-66
S10=(-21+15)×10/2=-30
S10-S6=36
T10=66+36=102

Let the sum of the first n terms of the arithmetic sequence an be Sn, if S4 / 12-s3 / 9 = 1, then the tolerance is?

Let the first term of the sequence be A1 and the tolerance be d,
Then S4 / 12-s3 / 9 = (4A1 + 10d) / 12 - (3A1 + 3D) / 9 = 1,
It is reduced to 5D / 6-D / 3 = 1,
The solution is d = 2

How much? The answer is different
cos²45°+tan60°cos30°

2

Calculation: sin 215 ° + cos 215 ° - cos 30 ° Tan 60 °

Sin215 ° + cos215 ° - cos30 ° tan60 ° = 1-32 × 3 (3 points) = 1-32 = − 12. (5 points)

Why is the range of y = / cos2x / [0,1]?

-1≤COS2X≤1
0≤/COS2X/≤1
The range of y = / cos2x / is [0,1]

What are the ranges of y = sin2x and y = cos2x

The ranges of y = sin2x and y = cos2x are [- 1,1]

The range of y = sin2x + cos2x-1 is

y=sin2x+cos2x-1
=√2*sin(2x+π/4)-1
So the range is [- √ 2-1, √ 2-1]

The period of the function y = sinxcosx is

y=sinxcosx
=(1/2)[2sinxcosx]
=(1/2)sin2x
The period is 2 π / 2 = π