In an arithmetic series a1 = - 14 and a5=30 find the sum of the first 5 terms

The sum of the 5 terms in the arithmetic series is 40.

Step-by-step explanation:

Step 1; First we need to determine the three values between a1 = - 14 and a5=30. The difference between the first and fifth value = 30 - (-14) = 30 + 14 = 44.

Since there are 4 values after a1 we divide the difference by the number of terms, the difference between each term = 44 / 4 = 11. So the difference between each term is 11.

Step 2; To find out the terms we just add the difference to the previous number.

a1 = - 14.

a2 = - 14 + 11 = - 3.

a3 = - 3 + 11 = 8.

a4 = 8 + 11 = 19.

a5 = 19 + 11 = 30.

So a1 + a2 + a3 + a4 + a5 = - 14 - 3 + 8 + 19 + 30 = 40.