1.) Use sigma notation to describe the sum of the first ten terms of the arithmetic sequence.

20+18.5+17+15.5+14+12.5+11+9.5+8+6.5

2.)Use sigma notation to describe the sum of the first ten terms of the geometric sequence.
(40)+(-10)+(5/2)+(-5/8)+(5/32)+(-5/126)+(5/512)+(-5/2046)+(5/8192)+(-5/32768)

9

∑ 20-1.5n
n=0

9
∑ 40(-1/4)^n
n=0

1.) The arithmetic sequence can be represented using sigma notation as follows:

∑ (20 + (n-1)(-1.5)), where n ranges from 1 to 10.

This means the sum of the arithmetic sequence is obtained by plugging in the numbers 1 to 10 for n and adding up the terms.

2.) The geometric sequence can be represented using sigma notation as follows:

∑ (40(-1/4)^(n-1)), where n ranges from 1 to 10.

This means the sum of the geometric sequence is obtained by plugging in the numbers 1 to 10 for n, evaluating the term using the given formula, and then adding up the terms.

1.) To describe the sum of the first ten terms of the arithmetic sequence, we can use sigma notation. Sigma notation is a way to compactly represent the sum of a sequence. It is represented by the Greek letter sigma (Σ) followed by the variable denoting the index of the term, a lower limit of the index, an upper limit of the index, and the expression giving the terms to be added.

In this case, the arithmetic sequence is given as: 20, 18.5, 17, 15.5, 14, 12.5, 11, 9.5, 8, 6.5.

To use sigma notation, we can let n be the index of the term. It starts from 1 and goes up to 10 because we are summing the first ten terms. The expression that gives the terms to be added is given by:

a_n = 20 + (1-n)*1.5

The lower limit of the index is 1, and the upper limit of the index is 10. So, we can write the sum of the first ten terms of the arithmetic sequence using sigma notation as:

Σ(a_n) from n = 1 to 10

2.) To describe the sum of the first ten terms of the geometric sequence, we can use sigma notation. Similar to the arithmetic sequence, sigma notation compactly represents the sum of a sequence. It is represented by the Greek letter sigma (Σ) followed by the variable denoting the index of the term, a lower limit of the index, an upper limit of the index, and the expression giving the terms to be added.

In this case, the geometric sequence is given as: 40, -10, 5/2, -5/8, 5/32, -5/126, 5/512, -5 /2046, 5/8192, -5/32768.

To use sigma notation, we can let n be the index of the term. It starts from 1 and goes up to 10 because we are summing the first ten terms. The expression that gives the terms to be added is given by:

a_n = 40 * (-1/4)^(n-1)

The lower limit of the index is 1, and the upper limit of the index is 10. So, we can write the sum of the first ten terms of the geometric sequence using sigma notation as:

Σ(a_n) from n = 1 to 10