Find the partial sum Sn of the arithmetic sequence that satisfies the given conditions.a2 = 5, a5 = 6.5, n = 16S16

To find the partial sum S16 of the arithmetic sequence, we first need to find the common difference (d) of the sequence.

The formula for the nth term of an arithmetic sequence is: an = a1 + (n - 1)d

We know that a2 = 5 and a5 = 6.5. We can set up the following equations:

5 = a1 + d (equation 1) 6.5 = a1 + 4d (equation 2)

Subtract equation 1 from equation 2 to find d:

6.5 - 5 = a1 + 4d - a1 - d 1.5 = 3d d = 1.5 / 3 = 0.5

Now that we have d, we can find a1 by substituting d into equation 1:

5 = a1 + 0.5 a1 = 5 - 0.5 = 4.5

Now we can find S16 using the formula for the sum of an arithmetic sequence:

S16 = n/2 * (a1 + an) S16 = 16/2 * (4.5 + a16)

To find a16, we use the formula for the nth term of an arithmetic sequence:

a16 = a1 + (16 - 1)d a16 = 4.5 + 15*0.5 = 4.5 + 7.5 = 12

Substitute a16 into the formula for S16:

S16 = 8 * (4.5 + 12) = 8 * 16.5 = 132

So, the partial sum S16 of the arithmetic sequence is 132.