Finding Terms in Arithmetic Sequences

This video tutorial explains how to solve a problem involving arithmetic sequences. The task is to find the first term (a1) and the common difference (D) given two terms of the sequence, a5 and a11. The video walks through the process of calculating D by setting up an equation using the given terms and solving for D. It then demonstrates how to find the first term using the calculated D. The tutorial concludes with a recap of the steps and emphasizes the key trick of subtracting subscripts to determine the number of times D is added.

What is the main objective of the problem discussed in the video?

• To find the product of terms in an arithmetic sequence

• To find the last term of an arithmetic sequence

• To find the first term and common difference of an arithmetic sequence

• To find the sum of an arithmetic sequence

Which terms are given in the problem to find the common difference?

• a1 and a5

• a1 and a11

• a5 and a11

• a2 and a10

How do you determine the number of times D is added to go from a5 to a11?

• By dividing the subscript of a11 by a5

• By adding the subscripts of a5 and a11

• By subtracting the subscript of a5 from a11

• By multiplying the subscripts of a5 and a11

What is the equation used to find D using a5 and a11?

• a11 = a5 + 7D

• a11 = a5 + 6D

• a11 = a5 + 4D

• a11 = a5 + 5D

What is the value of D after solving the equation?

• 9/2

• 7/2

• 5/2

• 3/2

What is the first step in finding the first term a1?

• Use a11 and subtract D

• Use a5 and add multiple of D

• Use a5 and add D

• Use a5 and subtract D

How many times is D added to a1 to reach a5?

• 6 times

• 5 times

• 4 times

• 3 times

What is the value of the first term a1?

• -29

• -25

• -31

• -27

What is the alternative method mentioned to find a1?

• Using a11 and subtracting D

• Using a11 and adding 10D

• Using a5 and adding 5D

• Using a5 and subtracting 4D

How many D's are added to a1 to reach a11 in the alternative method?

• 11 D's

• 10 D's

• 9 D's

• 8 D's