Question

Find a8 of the sequence 10, 9.75, 9.5, 9.25

Answer 1

The 8th term would be 8.25 because it decreases by .25 each term. 10,9.75, 9.5, 9.25, 9, 8.75, 8.5, 8.25

Answer 2

Good evening.

Let:

$\mathsf{a_1 = 10}\\ \mathsf{a_2=9.75}\\ \mathsf{a_3 = 9.5}\\ \mathsf{a_4 = 9.25}$

Note that:

$\mathsf{a_2 -a_1 = a_3-a_2=a_4-a_3 = -0.25 = r}$


Now we can make the General term formula:

$\mathsf{a_n= a_1 +(n-1)r}\\ \\ \boxed{\mathsf{a_n = 10 - (n-1)0.25}}$


Now we calculate a₈:


$\mathsf{a_8 = 10-(8-1)0.25}\\ \\ \mathsf{a_8 = 10 - 7\cdot0.25}\\ \\ \mathsf{a_8 = 10 - 1.75}\\ \\ \boxed{\boxed{\mathsf{a_8=8.25}}}$