Question 16

a10 - a1 = 18

The difference a10 - a1 equals 18 based on the established relationship in the sequence. Given that the sequence has a consistent pattern derived from the relationship of its terms, we can derive the necessary values.

A) 9

This option is incorrect because a10 - a1 cannot be as small as 9. The established relationship indicates a linear increase, and the difference must account for the full span of the sequence from a1 to a10.

B) 10

This choice is also incorrect. A difference of 10 suggests a much smaller increment between the terms than what is established by the relationship where a2 - a1 = 2, leading to a larger gap for a10.

C) 17

While this option is closer, it still does not account for the full progression of the sequence as dictated by the relationship. The increments based on the given conditions lead to a larger total difference.

D) 18

This is the correct option, as it accurately reflects the calculated difference based on the established relationship of the sequence. The terms increase consistently, leading to this specific difference.

E) 19

This option is incorrect because a difference of 19 exceeds the total calculated from the sequence progression. The derived value must align with the arithmetic nature of the sequence.

Conclusion

The correct difference a10 - a1 is 18, as determined by the arithmetic progression of the sequence. Other options fail to reflect the proper increments established by the relationship an = (an-1 + an+1)/2, confirming that D is the only valid answer.