Question

Write the first five terms of the sequence whose nth terms are: An = 2n- . 3n​

Answer 1

Answer:

next term = 5

Step-by-step explanation:

5,10,15,20...

Answer 2

Given:

• An Arithmetic Progression[AP] whose nth term is given by 2n - 3n.

Find:

• First 5 Terms of the AP.

Solution:

Let us first find the first 2 terms of the AP whose terms are given by the formula: 2n - 3n.

For n = 1:

a₁ = 2(1) - 3(1).

a₁ = 2 - 3.

a = a₁ = -1.

For n = 2:

a₂ = 2(2) - 3(2).

a₂ = 4 - 6.

a₂ = -2.

Now, common difference d is given by the formula:

$d = a_{n} - a_{n-1}$

So, the common difference in this case is:

d = a₂ - a₁.

d = -2 - (-1).

d = -2 + 1.

d = -1.

Now, let us check that -1 is the common difference.

We can do so by checking the difference of any 2 terms.[Other than the ones we have used already]

Finding the third term:

a₃ = 2(3) - 3(3).

a₃ = 6 - 9.

a₃ = -3.

Checking if our common difference is right:

d = a₂ - a₁ = a₃ - a₂.

a₂ - a₁ = -1.

a₃ - a₂ = -3 - (-2) = -3 + 2 = -1.

∴ a₂ - a₁ = a₃ - a₂.

∴ d = -1.

We know that the General Form of an AP is:

a, a+d, a+2d, a+3d, ...., a+(n-1)d.

Therefore, the first 5 terms of the AP are:

-1, -2, -3, -4, -5.