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Question
Write the sequence with nth term an = 6 − n
Solution
In the given problem, we are given the sequence with the nth term (`a_n`).
We need to show that these sequences form an A.P
an = 6 − n
So,
Substituting n = 1, we get
`a_1 = 6 -1`
`a_1 = 5`
Substituting n = 2, we get
`a_2 = 6 - 2`
`a_2 = 4`
Substituting n = 3, we get
`a_3 = 6 - 3`
`a_3 = 3`
Further, for the given to sequence to be an A.P,
Common difference (d) = `a_2 - a_1 = a_3 - a_2`
Here
`a_2 - a_1 = 4 - 5`
= -1
Also
`a_3 - a_2 = 3 - 4`
= -1
Since `a_2 - a_1 = a_3 - a_2`
Hence, the given sequence is an A.P
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