Answer:
a. 31/6; 33/6; 35/6
b. + 2/6
c. 37/6; 39/6; 41/6
d. 49/6
Explanation:
First we need to find the first three terms.
To do so solve the equations in the boxes.
When dividing by a fraction you multiply by the reciprocal so the equations are now as follows:
2 * 31/12
3 * 11/6
5 * 7/6
Solve these to get
62/12 = 31/6
33/6
35/6
The term to term rule as shown above is adding 2/6 or 1/3.
To find the next three terms in the sequence add 2/6 to the term.
35/6 + 2/6 = 37/6
37/6 + 2/6 = 39/6
39/6 + 2/6 = 41/6.
To find the 10th term you need to write out the arithmetic sequence equation.
an = a1 + (n-1)d
an is the term you want to find and n is the term number in this case that is 10. D is the common difference which in this case is 2/6. Plug these into the equation. A1 is the first term in the equation which in this case is 31/6.
31/6 + (10-1) 2/6
31/6 + (9)2/6
31/6 + 18/6 = 49/6