Question

Which sequence has constant 2nd differences?

O (5, 11.5, 18.5, 24.5}
O (0.5, 5, 12.5, 23)
O (-0.5, 5, 13.5, 23}
O (5, 13.5, 23, 34.5}

Answer 1

• 
  `O \: \: \: (0.5, 5, 12.5, 23)`

Task :

• To find out the sequence with constant 2nd differences

Solution :

In order to find the 2nd difference, we'll firstly find out the 1st differences by deducting the first term of each sequence from it's succeeding term and so on and then carry the same process to find the second differences.

sequence (1) : (5, 11.5, 18.5, 24.5)

1st differences

• 11.5 - 5 = 6.5
• 18.5 - 11.5 = 7
• 24.5 - 18.5 = 6

2nd differences

• 7 - 6.5 1.5
• 6 - 7 = -1

Thus, No ,this sequence don't have constant 2nd. differences

sequence (2) : (0.5, 5, 12.5, 23)

1st differences

• 5 - 0.5 = 4.5
• 12.5 - 5 = 7.5
• 23 - 12.5 = 10.5

2nd differences

• 7.5 - 4.5 = 3
• 10.5 - 7.5 = 3

Thus, Yes ,this sequence has constant 2nd differences.

sequence (3) : (-0.5, 5, 13.5, 23)

1st differences

• 5 -(-0.5) = 5.5
• 13.5 - 5 = 8.5
• 23 - 13.5 = 9.5

2nd differences

• 8.5 - 5.5 = 3
• 9.5 - 8.5 = 1

Thus,No, this sequence don't have constant 2nd differences.

sequence (4) : 5, 13.5, 23, 34.5)

1st differences

• 13.5 - 5 = 8.5
• 23-13.5 = 9.5
• 34.5 - 23 = 11.5

2nd differences

• 9.5 - 8.5 = 1
• 11.5 - 9.5 = 2

Thus, No ,this sequence don't have constant 2nd differences.