Write the sum using sigma notation.

Question

Write the sum using sigma notation.

1 + 3 + 5 +    + 29

__

E (____)

n = 1

Answer 1

Hello Rachel,

this is an arithmetic sequence starting at a₁ = 1 with a common difference of 2 (meaning you ADD 2 to go from one term to the next).

to find what position 29 occupies in the sequence, we use the formula a_n = a₁ + d(n-1) where we set a_n =29, d = 2, a₁ = 1 and solve for n which will give us the number to put on top of the sigma symbol.

29 = 1 + 2(n-1) ---> 28 = 2(n-1) ---> 14 = n-1 ---> n = 15

You now have everything you need to write the sum in sigma notation.

15 15

1 + 3 + 5 + .....+ 29 = ∑ (1 + 2(n-1)) = ∑ (2n - 1)

n = 1 n = 1

Answer 2

The summation 1+3+5+...+29 has a common difference of d=2 with the first term being a₁=1, so this can be written as the following arithmetic sequence:

a_n = a₁+(n-1)d --> a_n = 1+(n-1)(2) --> a_n = 1+2n-2 --> a_n = 2n-1

Now, we need to figure out what term 29 is, which can be solved with 29=2n-1, with solution n=15

In sigma notation, this would be ∑¹⁵_n=1 2n-1.

Hope this helped!