Arithmetic Sequences and Series

[eutas1]

Hello,
I have just been introduced to arithmetic sequences today, and I am confused on the question 1.(b) - please refer to my attachments.

It is not guaranteed that t3 will always be the third term of the sequence:
If the sequence was 1,2,3,4,5 then t3 would be 3 but;
If the sequence was 1,2,4,5,6 then t3 does not equal 4, it it still 3, it’s just that the person who wrote the sequence decided to exclude it...
So why isn’t 1.(b) an arithmetic sequence? t3 should be 9, not 12 since the difference is 3.....

 

[lev888]

Hello,
I have just been introduced to arithmetic sequences today, and I am confused on the question 1.(b) - please refer to my attachments.

It is not guaranteed that t3 will always be the third term of the sequence:
If the sequence was 1,2,3,4,5 then t3 would be 3 but;
If the sequence was 1,2,4,5,6 then t3 does not equal 4, it it still 3, it’s just that the person who wrote the sequence decided to exclude it...
So why isn’t 1.(b) an arithmetic sequence? t3 should be 9, not 12 since the difference is 3.....

No, t3 is the term actually used in the sequence. If it breaks the rule then the sequence is not arithmetic.

 

[eutas1]

No, t3 is the term actually used in the sequence. If it breaks the rule then the sequence is not arithmetic.

Oh what!!! I see.... thank you!

 

[HallsofIvy]

1(b) is a geometric sequence. Instead of adding the same thing to each term to get the next term, each term is multiplied by 2.