Express the following in Sigma notation
2+8+18+32+50+72
Calculate the difference between successive terms of the sum. The differences are the terms you need to add together to make the sum.
Sum: 2,8,18,32,50,72...
diff: 2,6,10,14,18,22...
0th term=2
1st term = 6
2nd term = 10
The rule is therefore 2+4i
So check if Σ2+4i works for you. i starts from zero.
My answer above applies if the list of numbers were successive sums.
Go with Reiny's answer:
http://www.jiskha.com/display.cgi?id=1262752887
Your sum equals 2(1+4+9+16+25+36), two times the sum of squares:
2 sum ( k^2) from 1 to 6
To express the given sequence in sigma notation, we need to identify the pattern or formula that generates each term. By looking at the given sequence, we can observe that each term is generated by adding a specific value to the previous term. Let's focus on the differences between adjacent terms:
8 - 2 = 6
18 - 8 = 10
32 - 18 = 14
50 - 32 = 18
72 - 50 = 22
From the differences, we can see that there is a pattern of increasing values by 4 each time. Therefore, we can express the sequence using the general term as:
a_n = a_1 + (n - 1) * 4
Here, a_n represents the n-th term of the sequence, a_1 is the first term, and n is the position of the term in the sequence.
Now, let's express the given sequence in sigma notation:
∑ [2 + (n - 1) * 4] from n = 1 to 6
In this notation, ∑ represents the summation symbol, the expression inside the square brackets represents the general term, and n = 1 to 6 indicates the range of values for which the general term is calculated.
Therefore, the given sequence can be expressed as:
∑ [2 + (n - 1) * 4] from n = 1 to 6