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प्रश्न
Write the sequence with nth term an = 5 + 2n
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 = 5 + 2n
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 = 5 + 2(1)`
`a_1 = 7`
Substituting n = 2, we get
`a_2 = 5 + 2(2)`
`a_2 = 9`
Substituting n = 3, we get
`a_3 = 5 + 2(3)`
`a_3 = 11`
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 = 9 - 7`
= 2
Also
`a_3 - a_2 = 11 - 9`
= 2
Since `a_2 - a_1 = a_3 - a_2`
Hence, the given sequence is an A.P
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