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प्रश्न
Write the sequence with nth term: an = 9 − 5n
उत्तर
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 = 9 − 5n
Now, to show that it is an A.P, we will find its few terms by substituting n = 1,2, 3
So
Substituting n = 1, we get`
`a_1 = 9 - 5(1)`
`a_1 = 4`
Substituting n = 2, we get
`a_2 = 9 - 5(2)
`a_2 = -1`
Substituting n = 3, we get
`a_3 = 9 - 5(3)`
`a_3 = -6`
Further, for the given sequence to be an A.P,
Common difference (d) = `a_2 - a_1 = a_3 - a_2`
Here
`a_2 - a_1 = -1 - 4
= -5
Also
`a_3 - a_2 = -6 - (-1)`
= -5
Since `a_2 - a_1 = a_3 - a_2`
Hence, the given sequence is an A.P.
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