Find the common difference of the Arithmetic Progression (A.P.)
1/a , 3-a/3a , 3-2a/3a,......('a' not equal to 0)
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Therefore, common difference = -1/3
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The common difference of the Arithmetic Progression (A.P.) is -1/3 of 1/a , (3 - a)/3a , (3 - 2a)/3a , ...
Given:
- Arithmetic Progression (A.P.)
- 1/a , (3 - a)/3a , (3 - 2a)/3a , ...
- a ≠ 0
To Find:
- The Common difference of the Arithmetic Progression (A.P.)
Solution:
- Arithmetic sequence
- Sequence of terms in which difference between one term and the next is a constant.
- This is also called Arithmetic Progression AP
- Arithmetic sequence can be represented in the form :
- a, a + d , a + 2d , …………………………, a + (n-1)d
- a = First term
- d = common difference = aₙ-aₙ₋₁
- nth term = aₙ = a + (n-1)d
- Sₙ = (n/2)(2a + (n - 1)d)
- Sum of Arithmetic sequence (AP) is called Arithmetic series
1/a , (3 - a)/(3a) , (3 - 2a)/(3a) , ...
Step 1:
Rewrite the term with common denominator 3a
3/(3a) , (3 - a)/(3a) , (3 - 2a)/(3a) , ...
Step 2:
Find Difference between consecutive terms
(3 - a)/(3a) - 3/(3a) = (3 - a - 3)/(3a) = -a/(3a) = -1/3
(3 - 2a)/(3a) - (3 - a)/(3a) = -1/3
Hence The common difference of the Arithmetic Progression (A.P.) is -1/3
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