Math  /  Algebra

QuestionSEKOTA COLLEGE OF TEACHERS EDUCATION MATHEMATICS DEPARTMENT Basic mathematics II(math: 102) test one 10%10 \% time Name \qquad IDNO cossin2Igg\cos ^{\circ} \sin ^{2} \mathrm{Ig}_{\mathrm{g}} Say true if the stetment is correct otherwise \qquad 1.A sequence is a function whose domain is the set of all real numb \qquad
2. {12,1,2,4,}\left\{\frac{1}{2}, 1,2,4, \ldots\right\} is example of Geometric sequence -
3. (1,2,3,4 )is example of Arithmetic sequence
4. A geometric sequence with q4=16\boldsymbol{q}_{\mathbf{4}}=16 and G1=2G_{\mathbf{1}}=2, the common ratic

Workout show the necessary steps each 2 Write the Difference between arithmetic and Geometric sequ re one example to each ve an Arithemetic sequence with a3=8,a5=15a_{3}=8, a_{5}=15, find a2a_{2} en a Geometric sequence G1=1G_{1}=1 and common ratio r=4r=4 fi

Studdy Solution
Given a geometric sequence G1=1 G_1 = 1 and common ratio r=4 r = 4 , find the next terms.
Use the general form of a geometric sequence: Gn=G1rn1 G_n = G_1 \cdot r^{n-1}
For G2 G_2 : G2=1421 G_2 = 1 \cdot 4^{2-1} G2=14 G_2 = 1 \cdot 4 G2=4 G_2 = 4
For G3 G_3 : G3=1431 G_3 = 1 \cdot 4^{3-1} G3=116 G_3 = 1 \cdot 16 G3=16 G_3 = 16
For G4 G_4 : G4=1441 G_4 = 1 \cdot 4^{4-1} G4=164 G_4 = 1 \cdot 64 G4=64 G_4 = 64
The next terms in the sequence are 4,16,64 4, 16, 64 .
Solution:
1. False
2. True
3. True
4. The common ratio is r=2 r = 2 .

Difference: - Arithmetic sequence: (3, 7, 11, 15, 19, ...) with d=4 d = 4 . - Geometric sequence: (3, 6, 12, 24, 48, ...) with r=2 r = 2 .
Given a3=8 a_3 = 8 and a5=15 a_5 = 15 : a2=4.5 a_2 = 4.5
Given G1=1 G_1 = 1 and r=4 r = 4 : Next terms: 4,16,64 4, 16, 64 .

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