Question 127
a) The first four terms of an infinite arithmetic sequence are given:
$$
-\frac{3}{2}, \frac{1}{2}, \frac{5}{2}, \frac{9}{2}
$$
Compute which number is the two-hundredth term of this sequence and what the sum of the first two hundred terms of the sequence is.
b) Between the numbers $\frac{1}{2}$ and $\frac{9}{2}$ we insert three numbers so that we obtain a geometric sequence. Determine all possible values of the inserted terms. The values should be exact.
$$
-\frac{3}{2}, \frac{1}{2}, \frac{5}{2}, \frac{9}{2}
$$
Compute which number is the two-hundredth term of this sequence and what the sum of the first two hundred terms of the sequence is.
b) Between the numbers $\frac{1}{2}$ and $\frac{9}{2}$ we insert three numbers so that we obtain a geometric sequence. Determine all possible values of the inserted terms. The values should be exact.