Question

A1=10,d=5 what is the sum of the first 12 terms?

Answer 1

450

Explanation:

To solve for the sum of the first n terms of an arithmetic series such as this, you must use the "NFL equation" :
`S = (n*(F+L))/2`

in which F (or A1) is the sequence's first term while L is the sequence's last term.

Although you can simply add each and every term in this series to get your answer, this trick provides a simpler process!

We know n and F (12 and 10 respectively), but L is unknown.

Simply multiply the common difference (d) with the number of terms minus 1 and add this product to the first term of the series:
`L = d*(n-1) + F`
`L = 5*(12-1)+10 = 65`

This equation basically adds 5 to 10 eleven times (one less than the number of terms, since the first term, 10, is included in the first twelve terms).

Now we may plug each of our values into the NFL equation to calculate the answer:
`S = (12*(10+65))/2 = 450`

450 is your final answer!