Answer:
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: