Question

A sequence starts with 7. The common difference is D. Write expressions for the next three terms in the sequence.

A sequence starts with 2. The common ratio is R. Write expressions for the next three terms in the sequence.

Answer 1

For the sequence that starts with 7 and has a common difference of D, the expression for the nth term of the sequence is:

a_n = 7 + (n-1)D

To find the next three terms in the sequence, we need to evaluate the expression for n = 2, n = 3, and n = 4.

So, the next three terms in the sequence are:

a_2 = 7 + (2-1)D = 7 + D

a_3 = 7 + (3-1)D = 7 + 2D

a_4 = 7 + (4-1)D = 7 + 3D

For the sequence that starts with 2 and has a common ratio of R, the expression for the nth term of the sequence is:

a_n = 2 x R^(n-1)

To find the next three terms in the sequence, we need to evaluate the expression for n = 2, n = 3, and n = 4.

So, the next three terms in the sequence are:

a_2 = 2 x R^(2-1) = 2R

a_3 = 2 x R^(3-1) = 2R^2

a_4 = 2 x R^(4-1) = 2R^3

Therefore, the expressions for the next three terms in the sequence starting with 7 and having a common difference of D are 7+D, 7+2D, and 7+3D.

And the expressions for the next three terms in the sequence starting with 2 and having a common ratio of R are 2R, 2R^2, and 2R^3.

Explanation:

Answer 2

You're on your own.. O-O