What is the 14th term of the arithmetic sequence -2x+8, 4x+2, 10x -4,....

Answer 1

Top find the value being added to each consecutive term, subtract two consecutive terms:

4x+2 - (-2x+8)

4x+2+2x-8 (by distribution to remove parentheses)

6x-6 (by combining like terms)

so d (the common difference) is 6x-6

The first term (a₁) is -2x+8

The equation the an arithmetic sequence is a_n = a₁ + (n-1)d so

a₁₄ = (-2x+8) + (14-1)(6x-6)

a₁₄ = 2x + 8 + 13(6x-6)

a₁₄ = 2x + 8 + 78x - 78

to get the final answer, combine like terms