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The 1st and the last term of an AP are –4 and 146. The sum of the terms is 7171. The number of terms is
- a)101
- b)100
- c)99
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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The 1st and the last term of an AP are –4 and 146. The sum of th...
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The 1st and the last term of an AP are –4 and 146. The sum of th...
Sn = n/2 ( a +b ) where a is first term and b is last term .
Now, 7171 = n/2 ( -4 +146)
14342 = n × 142
n = 14342 / 142
n = 101
Now, 7171 = n/2 ( -4 +146)
14342 = n × 142
n = 14342 / 142
n = 101
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The 1st and the last term of an AP are –4 and 146. The sum of th...
Given information:
- First term of AP = 4
- Last term of AP = 146
- Sum of terms = 7171
To find:
- Number of terms in the AP
Solution:
Let the number of terms in the AP be n.
Using the formula for the sum of an AP, we can write:
Sum of AP = (n/2) x [2a + (n-1)d]
where a is the first term, d is the common difference, and n is the number of terms.
Substituting the given values, we get:
7171 = (n/2) x [2x4 + (n-1)d]
7171 = n/2 x [8 + (n-1)d]
Dividing both sides by n/2, we get:
14342/n = 8 + (n-1)d
Rearranging, we get:
d = [14342/n - 8]/(n-1)
We also know that the first term a = 4 and the last term l = 146.
Using the formula for the nth term of an AP, we can write:
l = a + (n-1)d
Substituting the values, we get:
146 = 4 + (n-1)d
142 = (n-1)d
Dividing both sides by n-1, we get:
d = 142/(n-1)
Equating the two expressions for d, we get:
[14342/n - 8]/(n-1) = 142/(n-1)
Multiplying both sides by (n-1), we get:
14342/n - 8 = 142
Simplifying, we get:
n = 101
Therefore, the number of terms in the AP is 101.
Answer: (a) 101
- First term of AP = 4
- Last term of AP = 146
- Sum of terms = 7171
To find:
- Number of terms in the AP
Solution:
Let the number of terms in the AP be n.
Using the formula for the sum of an AP, we can write:
Sum of AP = (n/2) x [2a + (n-1)d]
where a is the first term, d is the common difference, and n is the number of terms.
Substituting the given values, we get:
7171 = (n/2) x [2x4 + (n-1)d]
7171 = n/2 x [8 + (n-1)d]
Dividing both sides by n/2, we get:
14342/n = 8 + (n-1)d
Rearranging, we get:
d = [14342/n - 8]/(n-1)
We also know that the first term a = 4 and the last term l = 146.
Using the formula for the nth term of an AP, we can write:
l = a + (n-1)d
Substituting the values, we get:
146 = 4 + (n-1)d
142 = (n-1)d
Dividing both sides by n-1, we get:
d = 142/(n-1)
Equating the two expressions for d, we get:
[14342/n - 8]/(n-1) = 142/(n-1)
Multiplying both sides by (n-1), we get:
14342/n - 8 = 142
Simplifying, we get:
n = 101
Therefore, the number of terms in the AP is 101.
Answer: (a) 101
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The 1st and the last term of an AP are –4 and 146. The sum of the terms is 7171. The number of terms isa)101b)100c)99d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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