Question

the algebraic form of an arithmetic sequence is 4n-1.
what is its common difference and what is it first term​

Answer 1

Required Answer:-

The algebraic form of an arithmetic sequence is given i.e. 4n - 1 where,

• n is the number of terms.
• Putting n = 1 will give the first term.

Then,

➙ First term = 4(1) - 1

➙ First term = 4 - 1

➙ First term = 3 (Ans - 1)

In a Arithmetic progression, there is a common difference between any two terms. So, we can determine d by finding two consecutive terms of the AP and subtracting them$.$

Putting n = 1

➙ a1 = 3 (We calculated earlier)

Putting n = 2

➙ a2 = 4(2) - 1

➙ a2 = 8 - 1

➙ a2 = 7

Then, common difference:

➙ d = a2 - a1

➙ d = 7 - 3

➙ d = 4 (Ans - 2)

Hence:-

The first term of the AP is 3 and the common difference is 4.

And we are done! :D

Answer 2

Answer:

Given :-

• An algebraic form AP = 4n - 1

To Find :-

Common difference

Solution :-

At first we will put n = 1

$\begin{gathered} \\ \end{gathered}$

⟹ First term = 4(1) - 1

⟹ First term = 4 - 1

⟹ First term = 3

Now,

Let's find Common Difference

⟹ a2 = 4(2) - 1

⟹ a2 = 8 - 1

⟹ a2 = 7

Now,

As we know that

Common Difference = A2 - A1

Common Difference = 7 - 3

⟹ Common Difference = 4