Arithmetic Sequences and Their Terms

The video tutorial explains how to find the first term and common difference of an arithmetic sequence given the 10th and 19th terms. It introduces two methods: treating the 10th term as the first term temporarily and using a system of equations. The video focuses on the latter, demonstrating how to set up and solve the equations to find the common difference and the first term. The process involves substitution, simplification, and elimination methods to solve the system of equations.

What are the given terms of the arithmetic sequence in the problem?

• 10th term is -22 and 19th term is 40

• 10th term is 22 and 19th term is -40

• 10th term is -40 and 19th term is 22

• 10th term is 40 and 19th term is -22

What is the first method suggested to solve the problem?

• Using a system of equations

• Assuming the 10th term as the first term

• Trial and error

• Graphical method

What is the formula for the nth term of an arithmetic sequence?

• a_n = a_1 + (n-1) * D

• a_n = a_1 * n + D

• a_n = a_1 / n + D

• a_n = a_1 - (n-1) * D

What is the equation formed for the 10th term?

• -22 = a_1 + 11D

• -22 = a_1 + 8D

• -22 = a_1 + 10D

• -22 = a_1 + 9D

What is the equation formed for the 19th term?

• -40 = a_1 + 18D

• -40 = a_1 + 19D

• -40 = a_1 + 17D

• -40 = a_1 + 20D

What method is used to solve the system of equations?

• Elimination

• Graphical

• Substitution

• Matrix

What is the common difference found in the sequence?

• -2

• 2

• -4

• 4

Which equation is used to find the first term after finding the common difference?

• -22 = a_1 + 10D

• -40 = a_1 + 18D

• -40 = a_1 + 19D

• -22 = a_1 + 9D

What is the first term of the sequence?

• 2

• 4

• -4

• -2

What is the final step to find the first term after substituting the common difference?

• Subtract 18 from both sides

• Add 18 to both sides

• Divide both sides by 18

• Multiply both sides by 18