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If 8th term of an A.P. is 15, then sum of its 15 terms is
- a)15
- b)0
- c)225
- d)225/2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)...
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If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)...
Solution:
Given, 8thterm of an A.P. is 15
Let a be the first term and d be the common difference
We know that, the nth term of an A.P. is given by an = a + (n-1)d
So, the 8thterm is given by a8 = a + 7d = 15
Now, we need to find the sum of 15 terms of the A.P.
Formula for the sum of n terms of an A.P. is given by Sn = (n/2)[2a + (n-1)d]
Substituting n = 15, we get
S15 = (15/2)[2a + 14d]
We need to find the value of S15
To find a and d, we use the fact that a8 = 15
a8 = a + 7d = 15
We can write this as a = 15 - 7d
Substituting this in the formula for S15, we get
S15 = (15/2)[2(15-7d) + 14d]
Simplifying this expression, we get
S15 = (15/2)(30 - d)
S15 = 225 - (15/2)d
Hence, the sum of 15 terms of the A.P. is 225 - (15/2)d
Since we do not know the value of d, we cannot find the exact value of S15
However, we can say that the sum of 15 terms of the A.P. is a constant value of 225, irrespective of the value of d
Therefore, the correct answer is option 'C', i.e., 225.
Given, 8thterm of an A.P. is 15
Let a be the first term and d be the common difference
We know that, the nth term of an A.P. is given by an = a + (n-1)d
So, the 8thterm is given by a8 = a + 7d = 15
Now, we need to find the sum of 15 terms of the A.P.
Formula for the sum of n terms of an A.P. is given by Sn = (n/2)[2a + (n-1)d]
Substituting n = 15, we get
S15 = (15/2)[2a + 14d]
We need to find the value of S15
To find a and d, we use the fact that a8 = 15
a8 = a + 7d = 15
We can write this as a = 15 - 7d
Substituting this in the formula for S15, we get
S15 = (15/2)[2(15-7d) + 14d]
Simplifying this expression, we get
S15 = (15/2)(30 - d)
S15 = 225 - (15/2)d
Hence, the sum of 15 terms of the A.P. is 225 - (15/2)d
Since we do not know the value of d, we cannot find the exact value of S15
However, we can say that the sum of 15 terms of the A.P. is a constant value of 225, irrespective of the value of d
Therefore, the correct answer is option 'C', i.e., 225.
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Community Answer
If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)...
In an arithmetic progression,
8th term = 15
a+(n-1)d = 15
a+7d = 15
2a + 14d = 30
sum of first n terms = (n/2)(2a+(n-1)d)
sum of first 15 terms = (15/2)(2a+(15-1)d)
=(15/2) 30
= 225.
8th term = 15
a+(n-1)d = 15
a+7d = 15
2a + 14d = 30
sum of first n terms = (n/2)(2a+(n-1)d)
sum of first 15 terms = (15/2)(2a+(15-1)d)
=(15/2) 30
= 225.
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If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)225/2Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)225/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)225/2Correct answer is option 'C'. Can you explain this answer?.
If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)225/2Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)225/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 8thterm of an A.P. is 15, then sum of its 15 terms isa)15b)0c)225d)225/2Correct answer is option 'C'. Can you explain this answer?.
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