In an arithmetic sequence, the sum of the first 8 terms is 88. The product of the 1st and the 8th terms is 120 .Calculate values for the 1st term

x = 8, x = 10

Step-by-step explanation:

= x - 7 ( square both sides )

4x - 31 = (x - 7)² ← expand using FOIL

4x - 31 = x² - 14x + 49 ( sub 4x - 31 from both sides )

0 = x² - 18x + 80 ← in standard form

0 = (x - 8)(x - 10) ← in factored form

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x - 10 = 0 ⇒ x = 10

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = 8

left side = = = = 1

right side = 8 - 7 = 1

Then x = 8 is a solution

x = 10

left side = = = = 3

right side = 10 - 7 = 3

Then x = 10 is a solution