What is the first term in the geometric progression (7, 21, 63, 189, ...)?
Answer and explanation
Correct answer: 7
The governing concept is identification of the first term in a geometric progression. When a sequence is written from left to right, its first term is the number at the beginning, usually denoted by a. The given progression begins with 7, so its first term is a = 7. The repeated multiplication by 3 is a separate property: 21 ÷ 7 = 3, 63 ÷ 21 = 3, and 189 ÷ 63 = 3, showing that the common ratio is 3. It does not alter the first term. Hence option B is correct. Options C and D are the second and third terms, respectively, while option A is the reciprocal of the common ratio, not a term of the displayed progression.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The governing concept is identification of the first term in a geometric progression. When a sequence is written from left to right, its first term is the number at the beginning, usually denoted by a. The given progression begins with 7, so its first term is a = 7. The repeated multiplication by 3 is a separate property: 21 ÷ 7 = 3, 63 ÷ 21 = 3, and 189 ÷ 63 = 3, showing that the common ratio is 3. It does not alter the first term. Hence option B is correct. Options C and D are the second and third terms, respectively, while option A is the reciprocal of the common ratio, not a term of the displayed progression.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
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