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Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term?
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Is 7 times the 7th term of an ap is equal to 11 times 11th term then f...
Given Information:
- 7 times the 7th term of an arithmetic progression (AP) is equal to 11 times the 11th term.
To Find:
- The 18th term of the arithmetic progression.
Solution:
Step 1: Understanding the Problem
- Let the first term of the AP be 'a' and the common difference be 'd'.
- The general form of the nth term of an AP is given by:
\[ T_n = a + (n-1)d \]
Step 2: Given Information
- According to the given information,
\[ 7(T_1 + 6d) = 11(T_1 + 10d) \]
\[ 7a + 42d = 11a + 110d \]
\[ 4a = 68d \]
\[ a = 17d \]
Step 3: Calculating the 18th Term
- We need to find the 18th term of the AP using the formula:
\[ T_{18} = a + 17d \]
\[ T_{18} = 17d + 17(17d) \]
\[ T_{18} = 17d + 289d \]
\[ T_{18} = 306d \]
Step 4: Final Answer
- Therefore, the 18th term of the arithmetic progression is 306d.
- 7 times the 7th term of an arithmetic progression (AP) is equal to 11 times the 11th term.
To Find:
- The 18th term of the arithmetic progression.
Solution:
Step 1: Understanding the Problem
- Let the first term of the AP be 'a' and the common difference be 'd'.
- The general form of the nth term of an AP is given by:
\[ T_n = a + (n-1)d \]
Step 2: Given Information
- According to the given information,
\[ 7(T_1 + 6d) = 11(T_1 + 10d) \]
\[ 7a + 42d = 11a + 110d \]
\[ 4a = 68d \]
\[ a = 17d \]
Step 3: Calculating the 18th Term
- We need to find the 18th term of the AP using the formula:
\[ T_{18} = a + 17d \]
\[ T_{18} = 17d + 17(17d) \]
\[ T_{18} = 17d + 289d \]
\[ T_{18} = 306d \]
Step 4: Final Answer
- Therefore, the 18th term of the arithmetic progression is 306d.
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Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term?
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Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term?.
Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is 7 times the 7th term of an ap is equal to 11 times 11th term then find its 18th term?.
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