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The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms?
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The first and last terms of an A. P are -4 and 146 and the sum is 7171...
Problem Statement: The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms.
Solution:
Let us assume that the number of terms in the given A.P. is 'n'.
Given, first term (a) = -4, last term (l) = 146 and sum (S) = 7171.
We know that the sum of an A.P. is given by the formula:
S = n/2[2a + (n-1)d]
where,
a = first term
l = last term
n = number of terms
d = common difference
Substituting the given values, we get:
7171 = n/2[-8 + (n-1)d + 292]
Simplifying the above equation, we get:
7171 = n/2[n + 284]
14342 = n^2 + 284n
n^2 + 284n - 14342 = 0
Solving the above quadratic equation, we get:
n = 50 or n = -334
Since the number of terms cannot be negative, we reject n = -334.
Therefore, the number of terms in the given A.P. is 50.
Answer: The number of terms in the given A.P. is 50.
Solution:
Let us assume that the number of terms in the given A.P. is 'n'.
Given, first term (a) = -4, last term (l) = 146 and sum (S) = 7171.
We know that the sum of an A.P. is given by the formula:
S = n/2[2a + (n-1)d]
where,
a = first term
l = last term
n = number of terms
d = common difference
Substituting the given values, we get:
7171 = n/2[-8 + (n-1)d + 292]
Simplifying the above equation, we get:
7171 = n/2[n + 284]
14342 = n^2 + 284n
n^2 + 284n - 14342 = 0
Solving the above quadratic equation, we get:
n = 50 or n = -334
Since the number of terms cannot be negative, we reject n = -334.
Therefore, the number of terms in the given A.P. is 50.
Answer: The number of terms in the given A.P. is 50.
Community Answer
The first and last terms of an A. P are -4 and 146 and the sum is 7171...
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The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms?
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The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms?.
The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first and last terms of an A. P are -4 and 146 and the sum is 7171. Find the number of terms?.
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