Question

The nth term of a quadratic sequence is an² + bn where a and b are integers. The second term of the sequence is 8, and the fifth term is 65. What is the value of the tenth term in the sequence?

Answer 1

The 10th term of the sequence is 280

Explanation:

When n = 2,

(2)²a + (2)b = 8.

=> 4a + 2b = 8.

When n = 5,

(5)²a + (5)b = 65.

=> 25a + 5b = 65.

4a + 2b = 8. => 10a + 5b = 20

25a + 5b = 65

- (10a + 5b = 20)

=> 15a = 45, a = 3.

Therefore 4(3) + 2b = 8, 2b = -4, b = -2.

We have a = 3 and b = -2.

Hence when n = 10,

an² + bn

= (10)²(3) + (10)(-2)

= 300 - 20

= 280.

Answer 2

Explanation:

When n = 2,

(2)²a + (2)b = 8.

=> 4a + 2b = 8.

When n = 5,

(5)²a + (5)b = 65.

=> 25a + 5b = 65.

4a + 2b = 8. => 10a + 5b = 20

25a + 5b = 65

- (10a + 5b = 20)

=> 15a = 45, a = 3.

Therefore 4(3) + 2b = 8, 2b = -4, b = -2.

We have a = 3 and b = -2.

Hence when n = 10,

an² + bn

= (10)²(3) + (10)(-2)

= 300 - 20

= 280.

The 10th term of the sequence is 280.