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Question
Write the sequence with nth term an = 5 + 2n
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 = 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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Activity :- Here a = 9, d = `square`
tn = a + (n − 1)d
t19 = 9 + (19 − 1) `square`
= 9 + `square`
= `square`
