Question

Find the sum of the first six terms in the sequence (1,5,9,13....)​

Answer 1

The sum is 66

Explanation:

There are a couple formulas to remember.

aₙ = a₁ + d(n-1)

Sₙ =
`(n)/(2)` · (a₁ + aₙ)

In your case "d" equals 4 and a₁ equals 1, that's how we know what the sequence will progress.

Let's plug in the values for the first equation:

aₙ = 1 + 4 (n-1)

Next we can simplify:

aₙ = 1 + 4n-4

aₙ = 4n - 3

Now we can plug in the value for "n" which is 6 for this particular problem:

a₆ = 4 · 6 - 3

a₆ = 21

We can now use the second equation to find the sum:

S₆ =
`(6)/(2)` · (1 + 21)

S₆ = 66

Hope this helps =)