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Question
Find a30 − a20 for the A.P.
a,a + d, a + 2d, a + 3d, ...
Solution
A.P. a,a + d, a + 2d, a + 3d, ...
Here
First term (a) = a
Common difference of the A.P (d) = a + d -a = d
Now as we know
`a_n= a + (n - 1)d`
Here we find `a_30` and `a_20`
So for 30 th term
`a_30 = a + (30 - 1)d`
`= a + (29)d`
Also for 20 th term
`a_20 = a + (20 - 1)d`
= a - (19)d
So,
`a_30 - a_20 = (a + 29d) - (a + 19d)`
= a + 29d - a - 19d
= 10d
Therefore for the given A.P `a_30 - a_20 = 10d`
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