Question

The third term in an arithmetic sequence is 3, and the common difference between each term is 4. Write a recursive formula for the sequence. A) an = 4an – 1 where a3 = 3 B) an = an – 1 + 4 where a3 = 3 C) an = an – 1 + 4 where a1 = 3 D) an = 3 + (n – 1) · 4 where a3 = 3

Answer 1

Given:

The third term in an arithmetic sequence is 3, and the common difference between each term is 4.

To find:

Write a recursive formula for the sequence.

A) an = 4an – 1 where a3 = 3

B) an = an – 1 + 4 where a3 = 3

C) an = an – 1 + 4 where a1 = 3

D) an = 3 + (n – 1) · 4 where a3 = 3

Solution:

From given, we have,

a3 = 3

d = 4

we use the formula for finding nth term of the sequence and is given by

an = a + (n - 1)d

a3 = a + (3 - 1)4

3 = a + (2) 4

3 = a + 8

a1 = a = -5

⇒ a2 = a1 + d = -5 + 4 = -1 .........(1)

⇒ a3 = a2 + d = -1 + 4 = 3 ........(2)

Therefore, the sequence is,

-5, -1, 3, 7, 11,........

Using (1) and (2), we get,

Therefore, option B) $a_n=a_{n-1}+4$ where a3 = 3 is the correct option.