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If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms?
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If the ratio of the 11th term of an AP to its 18 th term is 2:3, then ...
Given information:
The ratio of the 11th term to the 18th term of an AP is 2:3.
Let's solve step by step:
Step 1: Find the common difference (d) of the AP
Let the common difference of the AP be 'd'.
Using the formula for the nth term of an AP:
11th term = a + 10d
18th term = a + 17d
Given that the ratio of the 11th term to the 18th term is 2:3, we have:
(a + 10d)/(a + 17d) = 2/3
Solving this equation, we get d = 3
Step 2: Find the sum of the first 5 terms of the AP
The sum of the first n terms of an AP is given by the formula: Sn = n/2 [2a + (n-1)d]
For n=5, we have:
Sum of the first 5 terms = 5/2 [2a + 4d] = 5/2 [2a + 12] = 5a + 30
Step 3: Find the sum of the first 21 terms of the AP
For n=21, we have:
Sum of the first 21 terms = 21/2 [2a + 20d] = 21/2 [2a + 60] = 21a + 630
Step 4: Find the ratio of the sum of the first 5 terms to the sum of the first 21 terms
Ratio = (5a + 30)/(21a + 630) = 5/21
Therefore, the ratio of the sum of the first 5 terms to the sum of the first 21 terms is 5:21.
The ratio of the 11th term to the 18th term of an AP is 2:3.
Let's solve step by step:
Step 1: Find the common difference (d) of the AP
Let the common difference of the AP be 'd'.
Using the formula for the nth term of an AP:
11th term = a + 10d
18th term = a + 17d
Given that the ratio of the 11th term to the 18th term is 2:3, we have:
(a + 10d)/(a + 17d) = 2/3
Solving this equation, we get d = 3
Step 2: Find the sum of the first 5 terms of the AP
The sum of the first n terms of an AP is given by the formula: Sn = n/2 [2a + (n-1)d]
For n=5, we have:
Sum of the first 5 terms = 5/2 [2a + 4d] = 5/2 [2a + 12] = 5a + 30
Step 3: Find the sum of the first 21 terms of the AP
For n=21, we have:
Sum of the first 21 terms = 21/2 [2a + 20d] = 21/2 [2a + 60] = 21a + 630
Step 4: Find the ratio of the sum of the first 5 terms to the sum of the first 21 terms
Ratio = (5a + 30)/(21a + 630) = 5/21
Therefore, the ratio of the sum of the first 5 terms to the sum of the first 21 terms is 5:21.
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If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms?
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If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms?.
If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of the 11th term of an AP to its 18 th term is 2:3, then find the ratio of the sum of the first 5 terms to the sum of its first 21 terms?.
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