Question

The second and fourth numbers in an arithmetic sequences are 8 and 2. Find the first and the third numbers.

Answer 1

Second number in an arithmetic sequence = 8

Fourth number in an arithmetic sequence = 2

Let the first and the third number in the arithmetic sequence be x and y respectively.

Thus, the arithmetic sequence is x, 8, y, 2, …

⇒ y − 8 = 2 − y

⇒ y + y = 2 + 8

⇒ 2y = 10

⇒ y = 5

Also, 8 − x = y − 8

⇒ 8 − x = 5 − 8

⇒ x = 8 − 5 + 8

⇒ x = 11

Therefore, the first and the third number in the arithmetic sequence is 11 and 5 respectively.