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Write the Sequence With Nth Term: An = 3 + 4n - Mathematics

Write the sequence with nth term:

an = 3 + 4n

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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 = 1we get

`a_1 = 3 + 4(1)`

`a_1 = 7`

Substituting n = 2we get

`a_2= 3 + 4(2)`

`a_2 = 11`

Substituting n = 3we 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

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.2 | Q 4.1 | Page 8
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