Sum
If 5th and 6th terms of an A.P are respectively 6 and 5. Find the 11th term of the A.P
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Solution
The general term of an A.P is given by
`t_n = a + (n - 1)d`
Now `t_5 = 6`
=> a + (5 - 1)d = 6
=> a + 4d = 6 ....(i)
And `t_6 = 5`
=> a + (6 - 1)d = 5
=> a + 5d = 5 ...(ii)
Substracting (ii) from (i) we get
-d = 1
=> d = -1
Substituting d = -1 in (i) we get
a + 4(-1) = 6
=> a - 4 = 6
=> a = 10
`=> t_n = 10 + (n - 1)(-1)`
`=> t_11 = 10 + (11 - 1)(-1) = 10 - 10 = 0`
Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms.
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