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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Geometric progression

Grade: 9-a Lesson: S4-L8

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Find the \$5^(th)\$ terms the given geometric progression : 4,16,64,…
2	Step	To find the 5th term of the geometric progression, we need to determine the common ratio, r, of the sequence first. We can do this by dividing any term by the previous term:
3	Step	\$r = 16/4 = 4/1 = 64/16 = 4\$
4	Step	Since the common ratio is 4, we can use the formula for the nth term of a geometric sequence to find the 5th term: *\$a_n = a_1 r^(n-1)\$**
5	Step	Here, \$a_1\$ is the first term (4), r is the common ratio (4), and n is the term number we want to find (5) So, plugging in the values, we get:
6	Step	\$a_5 = 4 * 4^(5-1)\$ \$= 4 * 4^4\$ \$= 4 * 256\$ \$= 1024\$
7	Step	Therefore, the 5th term of the geometric progression 4, 16, 64, … is 1024
8		Answer	C

Step

Type

Explanation

Answer

Problem

Find the \$5^(th)\$ terms the given geometric progression : 4,16,64,…

Step

To find the 5th term of the geometric progression, we need to determine the common ratio, r, of the sequence first. We can do this by dividing any term by the previous term:

Step

\$r = 16/4 = 4/1 = 64/16 = 4\$

Step

Since the common ratio is 4, we can use the formula for the nth term of a geometric sequence to find the 5th term:

\$a_n = a_1 * r^(n-1)\$

Step

Here, \$a_1\$ is the first term (4), r is the common ratio (4), and n is the term number we want to find (5) So, plugging in the values, we get:

Step

\$a_5 = 4 * 4^(5-1)\$ \$= 4 * 4^4\$ \$= 4 * 256\$ \$= 1024\$

Step

Therefore, the 5th term of the geometric progression 4, 16, 64, … is 1024

Answer