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The sum of the 2nd and 5th terms of and A. P is 42.if the difference between the 6th and the 3rd is 12. Find the a. Common difference ?
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Mar 21
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#mathematics
#algebra
#arithmetic-progression
The sum of the 2nd and 5th terms of and A. P is 42.if the difference between the 6th and the 3rd is 12. Find the a. Common difference ?
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Mar 21
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Let the first term of the A.P be a and the common difference be d.
The 2nd term = a + d
The 5th term = a + 4d
The 6th term = a + 5d
The 3rd term = a + 2d
Given that the sum of the 2nd and 5th terms is 42:
(a + d) + (a + 4d) = 42
2a + 5d = 42
Given that the difference between the 6th and the 3rd terms is 12:
(a + 5d) - (a + 2d) = 12
3d = 12
d = 4
Substitute d = 4 into the first equation:
2a + 5(4) = 42
2a + 20 = 42
2a = 22
a = 11
Therefore, the common difference of the A.P is 4.
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