1.Write 4+6+8+10 in sigma notation:

I came up with sigma in the middle
3 on top
j=0 on the bottom
2n+4 to the right of the signma sign

2. Find the 10th term of the sequence
-1/5,-1/20,-1/80 this was a geometric sequence so I said a(subscript10) = -1/5*1/4^(10-1)
=-1/5*(1/4)^9 = -1/5*1/2621444
= -1/1310702

1. To write the expression 4+6+8+10 in sigma notation, you've correctly identified the use of the sigma symbol (∑) in the middle. However, the rest of the notation seems to be incorrect. Let me explain how to properly express it using sigma notation.

In sigma notation, the general form is ∑(expression, variable start, variable end), where the variable takes on values starting from the start value and increments by 1 until it reaches the end value. The expression represents the terms of the sequence.

For the given sequence 4+6+8+10, we can observe that each term is obtained by adding 2 to the previous term. So, the expression would be 2n + 2, where n represents the variable. The start value would be 0 (as the sequence starts from 4) and the end value would be 3 (as there are 4 terms in total).

Therefore, the sigma notation for 4+6+8+10 would be:
∑(2n + 2, 0, 3)

2. To find the 10th term of the geometric sequence -1/5, -1/20, -1/80, you've correctly identified that it's a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.

In this case, the common ratio is 1/4, as each term is obtained by multiplying the previous term by 1/4.

To find the 10th term (a₁₀) of this sequence, we can use the formula: aₙ = a₁ * r^(n-1), where a₁ represents the first term, r represents the common ratio, and n represents the term number.

In this case, the first term (a₁) is -1/5, the common ratio (r) is 1/4, and we want to find the 10th term (n = 10).

Plugging the values into the formula, we get:
a₁₀ = (-1/5) * (1/4)^(10-1)

Now we can simplify the expression:
a₁₀ = (-1/5) * (1/4)^9
a₁₀ = (-1/5) * (1/262144)
a₁₀ = -1/2621440

Therefore, the 10th term of the sequence is -1/2621440.