Question

The first term and common difference of some arithmetic sequence are given below. Write each of them in the form x_n = a_n + b; also write down the first three terms of each:

(i) first term −2, common difference 5

(ii) first term 2, common difference −5

(iii) first term 1, common difference

Answer 1

(i)

First term of the arithmetic sequence = a + b = −2 … (1)

Common difference = a = 5

Putting the value of a in equation (1):

5 + b = −2

⇒ b = −2 − 5 = −7

∴

Now, second term = 5(2) − 7 = 10 − 7 = 3

Third term = 5(3) − 7 = 15 − 7 = 8

Therefore, the first three terms of the given arithmetic sequence are −2, 3 and 8.

(ii)

First term of the arithmetic sequence = a + b = 2 … (1)

Common difference = a = −5

Putting the value of a in equation (1):

−5 + b = 2

⇒ b = 2 + 5 = 7

∴

Now, second term = −5(2) + 7 = −10 + 7 = −3

Third term = −5(3) + 7 = −15 + 7 = −8

Therefore, the first three terms of the given arithmetic sequence are 2, −3 and −8.

(iii)

First term of the arithmetic sequence = a + b = 1 … (1)

Common difference = a =

Putting the value of a in equation (1):

+ b = 2

∴

Now, second term =

Third term =

Therefore, the first three terms of the given arithmetic sequence are 2, and 3.