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Step-4

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 \$7^(th)\$ terms the given geometric progression : 3,9,27,…
2	Step	The common ratio (r) in this geometric progression can be found by dividing any term by the preceding term. Let’s use the second and first terms:
3	Step	\$r = 9/3 = 3\$
4	Step	To find the 7th term, we can use the formula for the nth term of a geometric progression: *\$a_n = a_1 r^(n-1)\$**
5	Step	where \$a_1\$ is the first term and n is the term we want to find Plugging in the given values, we get:
6	Step	\$a_7 = 3 * 3^(7-1) = 3 * 3^6 = 3 * 729 = 2187\$
7	Step	Therefore, the 7th term in the given geometric progression is 3,9,27,…2187
8		Answer	D

Step

Type

Explanation

Answer

Problem

Find the \$7^(th)\$ terms the given geometric progression : 3,9,27,…

Step

The common ratio (r) in this geometric progression can be found by dividing any term by the preceding term. Let’s use the second and first terms:

Step

\$r = 9/3 = 3\$

Step

To find the 7th term, we can use the formula for the nth term of a geometric progression:

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

Step

where \$a_1\$ is the first term and n is the term we want to find Plugging in the given values, we get:

Step

\$a_7 = 3 * 3^(7-1) = 3 * 3^6 = 3 * 729 = 2187\$

Step

Therefore, the 7th term in the given geometric progression is 3,9,27,…2187

Answer