Example of Practice Questions on Geometric Sequences and Series, Grade 10, Phase E

The following is an example of a geometric series problem for grade 10, phase e, number elements, which you can study complete with a discussion.

Geometric Sequences and Series is a continuation of Sequences and series after we previously studied Arithmetic Sequences and Series↝ . This material in mathematics lessons is part of the number elements. You certainly learned this material in grade X Phase E. For those of you who have not studied the theory, please study Geometric Sequences and Series↝

Here are some examples of questions and their discussion.

Example of Geometry Line Question Exercise

1. The geometric line $9,3,1,\frac{1}{3},…$ is known

   The 7th quarter of the line is

   1. $\frac{1}{243}$
   2. $\frac{1}{81}$
   3. $\frac{1}{27}$
   4. $\frac{1}{72}$
   5. $\frac{1}{64}$

      Solution ✍️

      Ans: B

2. The ratio of the row $\frac{27}{16},\frac89,\frac43, 2, …$ is …

   1. $\frac34$
   2. $\frac43$
   3. $\frac32$
   4. $\frac23$
   5. $\frac13$

3. It is known that the row $√3 , 3, 3√3 , …$ The 9th quarter is …

   1. $81 \sqrt3$
   2. $81$
   3. $243$
   4. $612 \sqrt3$
   5. $729$

4. The formula of the nth term from the row $100, 20, 4, \dfrac45, …$ is …

   1. $U_n = 4. 5^{n-1}$
   2. $U_n = 4. 5^{n-2}$
   3. $U_n = 4. 5^{n-3}$
   4. $U_n = 4. 5^{n+3}$
   5. $U_n = 4. 5^{3-n}$

5. A geometric sequence is known to have a 3rd term and a 6th term of 81. Then the 8th term is…

   1. 729
   2. 612
   3. 542
   4. 712
   5. 681

6. Given the sequence 2, 2 2 , 4, 4 2 , … What term is $64\sqrt2$ ?

   1. 11
   2. 12
   3. 13
   4. 14
   5. 1

7. A motorbike is purchased for Rp20,000,000.00, and its resale value decreases by 3/4 of its original value every year. The resale value of the motorbike after 3 years is…

   1. Rp6.328.125,00
   2. Rp8,437,500.00
   3. Rp8,750,000.00
   4. Rp11,250,000.00
   5. Rp11,562,500.00

Example Practice Questions on Geometric Series

1. The sum of the first 5 terms of the series 3 + 6 + 12 + … is …
   1. 62
   2. 84
   3. 93
   4. 108
   5. 152
2. The sum of the first n terms of a geometric series is expressed as $S_n = 2^{n+2} – 3$. The formula for the nth term is…
   1. $2^{n–1}$
   2. $2^{n+1}$
   3. $2^{n+3}$
   4. $2^{n–3}$
   5. $2^n$
3. Given a geometric series with the first term being 6 and the fourth term being 48. The sum of the first six terms of the series is…
   1. 368
   2. 369
   3. 378
   4. 379
   5. 384
4. Four numbers are known, the first three numbers are geometric rows and the last three numbers are geometric series. The sum of the second number and the fourth is 10. The sum of the first and third numbers is 18. The sum The four numbers are…
   1. 28
   2. 31
   3. 44
   4. 52
   5. 81
5. A piece of rope is cut into 8 pieces. The length of each piece is follows a geometric sequence. The length of the shortest piece of rope is 4 cmand the length of the longest piece of rope is 512 cm. Strap length again is … cm
   1. 512
   2. 1020
   3. 1024
   4. 2032
   5. 2048

Example Practice Questions on Infinite Geometric Series

1. The sum to infinity of the geometric series $4+2+1+\dfrac12+⋯$ is …
   1. 6
   2. 8
   3. 10
   4. 12
   5. 13

      Solution ✍️

      Ans: B
2. The sum of an infinite geometric series is 81. If the ratio is $\dfrac23$, then the third term is…
   1. 32
   2. 24
   3. 18
   4. 16
   5. 12
3. The sum of an infinite geometric series is 10. If the first term is 2, the second term is 10. the series is…
   1. $\dfrac15$
   2. $\dfrac45$
   3. $1$
   4. $1\dfrac15$
   5. $1\dfrac35$
4. A swing reaches a first trajectory of 90 cm and the next trajectory is 90 cm. only reaches $\frac58$ of the previous trajectory. The total length of the trajectory until the swing stops is … cm
   1. 120
   2. 144
   3. 240
   4. 250
   5. 260
5. A rolling ball is slowed down at a certain speed. At the 1st second the distance traveled is 8 meters, in the 2nd second the distance traveled is 6 meters, in 3rd second the distance covered is 4.5 meters, and so on following the line pattern geometry. The distance the ball travels until it stops is … meters
   1. 32
   2. 28
   3. 24
   4. 22,5
   5. 20,5