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In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find
(a) common ratio (b) first term (c) sum of the first five terms of G.P?
(a) common ratio (b) first term (c) sum of the first five terms of G.P?
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In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the ...
Given information:
- 5th term exceeds the 4th term by 24
- 4th term exceeds the 3rd term by 8
Let's solve the problem step by step:
Step 1: Find the common ratio (r)
- Let the first term be 'a', common ratio be 'r'
- According to the given information: 4th term = a * r^3, 5th term = a * r^4
- Given: a * r^4 - a * r^3 = 24
- Simplifying: a * r^3 * (r - 1) = 24
- Given: a * r^3 - a * r^2 = 8
- Substituting this value in the above equation: (a * r^3) * (r - 1) = 3a = 24
- Solving for 'a', we get a = 8, then r = 2
Step 2: Find the first term (a)
- Using the common ratio 'r' we found, a = 8
Step 3: Find the sum of the first five terms of the G.P
- Sum of first five terms = a * (r^5 - 1) / (r - 1)
- Substituting the values of 'a' and 'r', we get sum = 8 * (2^5 - 1) / (2 - 1) = 248
Therefore,
(a) Common ratio (r) = 2
(b) First term (a) = 8
(c) Sum of the first five terms of G.P = 248
- 5th term exceeds the 4th term by 24
- 4th term exceeds the 3rd term by 8
Let's solve the problem step by step:
Step 1: Find the common ratio (r)
- Let the first term be 'a', common ratio be 'r'
- According to the given information: 4th term = a * r^3, 5th term = a * r^4
- Given: a * r^4 - a * r^3 = 24
- Simplifying: a * r^3 * (r - 1) = 24
- Given: a * r^3 - a * r^2 = 8
- Substituting this value in the above equation: (a * r^3) * (r - 1) = 3a = 24
- Solving for 'a', we get a = 8, then r = 2
Step 2: Find the first term (a)
- Using the common ratio 'r' we found, a = 8
Step 3: Find the sum of the first five terms of the G.P
- Sum of first five terms = a * (r^5 - 1) / (r - 1)
- Substituting the values of 'a' and 'r', we get sum = 8 * (2^5 - 1) / (2 - 1) = 248
Therefore,
(a) Common ratio (r) = 2
(b) First term (a) = 8
(c) Sum of the first five terms of G.P = 248
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In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find(a) common ratio (b) first term (c) sum of the first five terms of G.P?
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In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find(a) common ratio (b) first term (c) sum of the first five terms of G.P? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find(a) common ratio (b) first term (c) sum of the first five terms of G.P? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find(a) common ratio (b) first term (c) sum of the first five terms of G.P?.
In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find(a) common ratio (b) first term (c) sum of the first five terms of G.P? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find(a) common ratio (b) first term (c) sum of the first five terms of G.P? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a G.P 5th term exceeds the 4th term by 24 and 4th term exceeds the 3rd term by 8. Find(a) common ratio (b) first term (c) sum of the first five terms of G.P?.
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