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Question
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
Options
11
3
8
5
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Solution
Here, we are given two A.P.’s with same common difference. Let us take the common difference as d.
Given,
First term of first A.P. (a) = 8
First term of second A.P. (a’) = 3
We need to find the difference between their 30th terms.
So, let us first find the 30th term of first A.P.
`a_30 = a + ( 30 -1) d`
= 8 + 29 d ...........(1)
Similarly, we find the 30th term of second A.P.
`a'_(30) = a '+ ( 30 -1) d`
= 3 + 29 d ...............(2)
Now, the difference between the 30th terms is,
`a_30 - a'_(30) = (8 + 29d) - ( 3 + 29 d) `
= 8 + 29 d - 3 - 29 d
= 8 -3
= 5
Therefore, `a_30 - a'_(30) = 5`
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