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The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?
- a)346
- b)340
- c)304
- d)268
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The sum of the first four terms of an AP is 28 and sum of the first ei...
Think like this:
The average of the first 4 terms is 7, while the average of the first 8 terms must be 11.
Now visualize this :
The average of the first 4 terms is 7, while the average of the first 8 terms must be 11.
Now visualize this :
Hence, d = 4/2 = 2 [Note: understand this as a property of an A.P.]
Hence, the average of the 6th and 7th terms = 15 and the average of the 8th and 9th term = 19
But this (19) also represents the average of the 16 term A.P.
Hence, required answer = 16 × 19 = 304.
Hence, the average of the 6th and 7th terms = 15 and the average of the 8th and 9th term = 19
But this (19) also represents the average of the 16 term A.P.
Hence, required answer = 16 × 19 = 304.
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The sum of the first four terms of an AP is 28 and sum of the first ei...
Given information:
- Sum of the first four terms of an AP is 28
- Sum of the first eight terms of the same AP is 88
To find:
- Sum of the first 16 terms of the AP
Solution:
Let the first term of the AP be 'a' and the common difference be 'd'.
Using the formula for sum of first 'n' terms of an AP:
- Sum of first four terms = (4/2) [2a + (4-1)d] = 2[2a + 3d] = 28
- Sum of first eight terms = (8/2) [2a + (8-1)d] = 4[2a + 7d] = 88
Solving these two equations simultaneously, we get:
a = 5, d = 3
Now, using the formula for sum of first 'n' terms of an AP:
- Sum of first 16 terms = (16/2) [2a + (16-1)d] = 8[2a + 15d] = 8[2(5) + 15(3)] = 304
Therefore, the sum of the first 16 terms of the AP is 304, which is option (c).
- Sum of the first four terms of an AP is 28
- Sum of the first eight terms of the same AP is 88
To find:
- Sum of the first 16 terms of the AP
Solution:
Let the first term of the AP be 'a' and the common difference be 'd'.
Using the formula for sum of first 'n' terms of an AP:
- Sum of first four terms = (4/2) [2a + (4-1)d] = 2[2a + 3d] = 28
- Sum of first eight terms = (8/2) [2a + (8-1)d] = 4[2a + 7d] = 88
Solving these two equations simultaneously, we get:
a = 5, d = 3
Now, using the formula for sum of first 'n' terms of an AP:
- Sum of first 16 terms = (16/2) [2a + (16-1)d] = 8[2a + 15d] = 8[2(5) + 15(3)] = 304
Therefore, the sum of the first 16 terms of the AP is 304, which is option (c).
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The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?a)346b)340c)304d)268Correct answer is option 'C'. Can you explain this answer?
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The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?a)346b)340c)304d)268Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?a)346b)340c)304d)268Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?a)346b)340c)304d)268Correct answer is option 'C'. Can you explain this answer?.
The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?a)346b)340c)304d)268Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?a)346b)340c)304d)268Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88.Find the sum of the first 16 terms of the AP?a)346b)340c)304d)268Correct answer is option 'C'. Can you explain this answer?.
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