Express the following in Sigma notation
2+8+18+32+50+72
hint:
2+8+18+32+50+72
= 2(1^2) + 2(2^2) + 2(3^2) + 2(4^2) + 2(5^2) + 2(6^2)
Can you finish it?
To express the given series in Sigma notation, let's observe the pattern of the terms:
2, 8, 18, 32, 50, 72
We notice that each term is formed by adding a multiple of 6 to the previous term:
2 + 6 = 8, 8 + 10 = 18, 18 + 14 = 32, 32 + 18 = 50, 50 + 22 = 72
Therefore, we can express the series in Sigma notation as follows:
∑(n=1 to 6) (2 + 6(n-1))
Let's break down the components of this notation:
- The Σ symbol represents the sum.
- 'n=1' denotes the starting value of the index.
- 'n=6' denotes the ending value of the index.
- (2 + 6(n-1)) represents the formula for each term.
Thus, the given series can be expressed in Sigma notation as:
∑(n=1 to 6) (2 + 6(n-1))