Question

Find the common difference and write the next four terms of each of the following arithmetic progressions:

(i) 1, −2, −5, −8, ...

(ii) 0, −3, −6, −9, ...

(iii) $-1,\frac{1}{4},\frac{3}{2},...$

(iv) $-1,\frac{5}{6},\frac{2}{3},...$

Answer 1

In the given problem, we need to find the common difference and the next four terms of the given A.P.

(i)

Here, first term (a₁) =1

Common difference (d)

Now, we need to find the next four terms of the given A.P

That is we need to find

So, using the formula

Substituting in the above formula

Substituting n = 5, we get

Substituting n = 6, we get

Substituting n = 7, we get

Substituting n = 8, we get

Therefore, the common difference is and the next four terms are

(ii)

Here, first term (a₁) =0

Common difference (d)

Now, we need to find the next four terms of the given A.P

That is we need to find

So, using the formula

Substituting in the above formula

Substituting n = 5, we get

Substituting n = 6, we get

Substituting n = 7, we get

Substituting n = 8, we get

Therefore, the common difference is and the next four terms are

(iii)

Here, first term (a₁) =−1

Common difference (d)

Now, we need to find the next four terms of the given A.P

That is we need to find

So, using the formula

Substituting in the above formula

Substituting n = 4, we get

Substituting n = 5, we get

Substituting n = 6, we get

Substituting n = 7, we get

Therefore, the common difference is and the next four terms are

(iv)

Here, first term (a₁) =−1

Common difference (d)

Now, we need to find the next four terms of the given A.P

That is we need to find

So, using the formula

Substituting in the above formula

Substituting n = 4, we get

$$\begin{gathered} a_4=-1+\left(4-1\right)\left(\frac{1}{6}\right) \\ {a}_4=-1+\left(\frac{1}{2}\right) \\ {a}_4=\frac{-2+1}{2}=\frac{-1}{2} \end{gathered}$$

Substituting n = 5, we get

Substituting n = 6, we get

Substituting n = 7, we get

Therefore, the common difference is and the next four terms are