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In the arithmetic sequence {an}, if A1 = 3, A100 = 36, then A37 =?
Thirteen
When a takes what value, the linear equations (x1 + x2 + X3 = a, ax1 + x2 + X3 = 1, X1 + x2 + AX3 = 1) have solutions
The rank of the coefficient matrix is equal to that of the augmented matrix: 111a-1100a-1 by elementary row column transformation. We can get 111a-1100a-1 augmented matrix 111aa-111a1 by elementary row column transformation. When a = 1
In △ ABC, D is the midpoint of BC, e and F are on AB and AC respectively, and de ⊥ DF. The quantitative relationship among be, CF and EF is judged and proved
Answer: be + CF ＞ EF. Prove: as shown in the figure, extend ed to P, so that DP = De, connect FP, CP,
RELATED INFORMATIONS
- 1. As shown in the figure, BD and CE are the two heights of triangle ABC, and m and N are the midpoint of BC and de respectively
- 2. It is known that [an] and {BN} are arithmetic sequences, and CN = 3an + 2. It is proved that {CN} is also arithmetic sequences (2) The second question CN = an + BN (AB is not equal to 0): the sequence {CN} is an arithmetic sequence
- 3. In the RT triangle ABC, the angle BAC = 90, ad ⊥ BC at point D, e is the midpoint of AD, the extension line connecting ed and intersecting AB at point F, AB / AC = DF / AF is proved E is the midpoint of AC
- 4. Let an and BN satisfy A1 = B1 = 6, A2 = B2 = 4, A3 = B3 = 3, and a (n + 1) - an (n belongs to positive integer) is an arithmetic sequence Let an and BN satisfy A1 = B1 = 6, A2 = B2 = 4, A3 = B3 = 3, and a (n + 1) - an (n is a positive integer) is an arithmetic sequence, Sn is the sum of the first several terms of the sequence {BN}, and Sn = 2n-bn + 101) is the general term formula of an and BN (2) Does K belong to a positive integer, so that AK BK belongs to (0,1 / 2)? If so, find K; if not, explain the reason
- 5. In △ ABC, extend the midline BD on the AC side to F, so that DF = BD, extend the midline CE on the AB side to g, so that eg = CE
- 6. (1) In the plane rectangular coordinate system, move point a (- 3,4) to the right 5 units to point A1, and then rotate point A1 clockwise 90 ° around the origin of the coordinate to point A2. Directly write out the coordinates of points A1 and A2; (2) in the plane rectangular coordinate system, move point B (a, b) in the second quadrant to the right m units to point B1 in the first quadrant, and then rotate point B1 clockwise 90 ° around the origin of the coordinate to point B 2. Directly write out the coordinates of points B1 and B2; (3) in the plane rectangular coordinate system, translate point P (C, d) n units along the horizontal direction to point P1, and then rotate point P1 90 ° clockwise around the origin of the coordinate to point P2, directly write out the coordinates of point P2
- 7. [help] there is a point P in the triangle ABC, which satisfies "vector PA + vector Pb + vector PC = 0". Can you explain that P is the center of gravity of the triangle ABC?
- 8. The midpoint o (0,0) and a (2,0) B of the plane rectangular coordinate system are the midpoint of the line OA. Rotate OA clockwise about point O for 30 degrees. Mark the corresponding point of point B as C, and find the location of point C
- 9. As shown in the figure, in △ ABC, ∠ B = 90 °, M is the point on AB, so that am = BC, n is the point on BC, so that CN = BM, connecting an and cm intersects at P, try to find the degree of ∠ APM
- 10. Given that the negative integer solution of inequality x-m > 0 is - 1, - 2, - 3, - 4, find the value range of M (and draw the number axis) It's OK not to draw, but it's not easy to write
- 11. As shown in the figure, in △ ABC, D is the midpoint of BC, de ⊥ AB is at e, DF ⊥ AC is at F, and be = CF
- 12. The N-1 power {BN} of an and Sn = 2-1 / 2 is the arithmetic sequence A1 = B1, A2 * (b2-b1) = A1 to find the general term of BN? Let CN = BN / an to find the general term of CN
- 13. In the RT triangle ABC, the angle c = 90, BC = a, AC = B, a + B = 16, then the function analysis of the area s of the RT triangle with respect to the variable length a When s = 32, a=______
- 14. It is known that the equal ratio sequence satisfies A1 = 2, A2 + a3 = 12 and A4 > 0.1. Find the general term formula of sequence an. 2. If BN = anlog2an, the first n term of sequence BN is SN The main thing is to ask the second question!
- 15. If AQ = 1 / mAb, AP = 1 / NAC, then M + n is equal to A.1 B.2 C.3 D.4
- 16. In the known sequence an, A1 = 2, the sum of the first n terms is SN. For any n ≥ 2, 3sn-4, an, 2-3 / 2S (n-1) is an arithmetic sequence (1) (2) if BN satisfies BN = 3Sn, find the first n terms and TN of BN
- 17. Ad is the height of the side BC of the triangle ABC. Take ad as the diameter to make a circle, intersect with AB and AC respectively, multiply AC by E and F, and prove that AE multiplied by ab equals AF
- 18. Let BN = an + n prove that {BN} is an equal ratio sequence
- 19. In the triangle ABC, D is the midpoint of BC, AE bisector angle BAC, make de perpendicular to AE at e, intersect AB at g, intersect AC extension line at h. proof: BG = ch = 1 / 2 (AB-AC)
- 20. In the equal ratio sequence {an}, for any natural number n, there are a1 + A2 + +An = 2 ^ n-1, then (A1) ^ 2 + (A2) ^ 2 + +（an）^2=?