Question

if the third and fourth term of a sequence are A3 = 2 and A4 =8 determine the common difference as well as the first and second terms​

Answer 1

The common difference is 6. The first term is -10 and the second term is -4.

Step-by-step explanation:

To determine the common difference and the first and second terms of the sequence, we can use the formula for the nth term of an arithmetic sequence: An = A1 + (n - 1)d.

Given that A3 = 2 and A4 = 8, we can substitute these values into the formula:

A3 = A1 + (3 - 1)d = 2

A4 = A1 + (4 - 1)d = 8

Simplifying these equations, we get:

A1 + 2d = 2

A1 + 3d = 8

Subtracting the second equation from the first equation, we get:

(A1 + 2d) - (A1 + 3d) = 2 - 8

-d = -6

Therefore, the common difference is d = 6.

Substituting the value of d in either of the original equations, we get:

A1 + 2(6) = 2

A1 + 12 = 2

A1 = -10

So, the first term is -10 and the second term can be found by substituting A1 and d into the formula:

A2 = A1 + (2 - 1)d = -10 + 1(6) = -10 + 6 = -4.