Question

Find the next five terms of each of the following sequences given by:

(i) a₁ = 1, a_n = a_n−1+2, n ≥ 2

(ii) a₁ = a₂ = 2, a_n = a_n−1 − 3, n > 2

(iii) $a_1=-1,a_n=\frac{a_n-1}{n},n\ge 2$

(iv) a₁ = 4, a_n = 4a_n−1 + 3, n > 1.

Answer 1

In the given problem, we are given the first, second term and the n^th term of an A.P.

We need to find its next five terms

(i) , ,

Here, we are given that

So, the next five terms of this A.P would be,, , and

Now …… (1)

So, to find theterm we use, we get,

(Using 1)

…… (2)

For, using, we get,

(Using 2)

…… (3)

For, using, we get,

(Using 3)

…… (4)

For, using, we get,

(Using 4)

……. (5)

For, using, we get,

(Using 5)

Therefore, the next five terms, of the given A.P are

(ii) , ,

Here, we are given that

So, the next five terms of this A.P would be,,,and

Now …… (1)

So, to find theterm we use, we get,

(Using 1)

…… (2)

For, using, we get,

(Using 2)

…… (3)

For, using, we get,

(Using 3)

…… (4)

For, using, we get,

(Using 4)

…… (5)

For, using, we get,

(Using 5)

Therefore, the next five terms, of the given A.P are

(iii) , ,

Here, we are given that

So, the next five terms of this A.P would be, ,, and

Now …… (1)

So, to find theterm we use, we get,

(Using 1)

…… (2)

For, using, we get,

(Using 2)

…… (3)

For, using, we get,

(Using 3)

…… (4)

For, using, we get,

(Using 4)

…… (5)

For, using, we get,

(Using 5)

Therefore, the next five terms, of the given A.P are

(iv) , ,

Here, we are given that n > 1.

So, the next five terms of this A.P would be, , , and

Now …… (1)

So, to find theterm we use, we get,

(Using 1)

…… (2)

For, using, we get,

(Using 2)

…… (3)

For, using, we get,

(Using 3)

…… (4)

For, using, we get,

(Using 4)

…… (5)

For, using, we get,

(Using 5)

Therefore, the next five terms, of the given A.P are