Question

5. Which expression defines the arithmetic series 1 + 3 + 5 +... for seven terms?Σ(27-1)Σ(n-1)OΣ2ηO2n-1

Answer 1

We have the following expression 1 + 3 + 5 +... until the 7th term.

Each term equals the previous term plus 2.

So, for any term of number n, we have:

`a_(n+1)=a_1+n\cdot r_{}`

In this case, r = 2.

The sum of all therms of an arithmetic progression with 7 terms and a diference r between two consecutive terms is:

`\sum ^7_(n\mathop=1)a_1+(n-1)\cdot r`

For a1 = 1 and r = 2, we got:

`\sum ^7_(n\mathop=1)2n-1_{}`