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Question
Write the sequence with nth term:
an = 3 + 4n
Solution
In the given problem, we are given the sequence with the nth term `(a_n)`.
an = 3 + 4n
Now, to show that it is an A.P, we will first find its few terms by substituting n = 1, 2.3
So,
Substituting n = 1, we get
`a_1 = 3 + 4(1)`
`a_1 = 7`
Substituting n = 2, we get
`a_2= 3 + 4(2)`
`a_2 = 11`
Substituting n = 3, we get
`a_3 = 3 + 4(3)`
`a_3 = 15`
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 = 11 - 7
= 4
Also
`a_3 - a_2 = 15 - 11`
= 4
Since `a_2 - a_1 = a_3 - a_2`
Hence, the given sequence is an A.P
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