Question

Determine whether each of the following sequences are arithmetic, geometric or neither. If arithmetic, state the common difference. If geometric, state the common ratio. -29, -34, -39, -44, -49, ...
Is this: common difference =5?
arithmetic?

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}$

$\textbf{Let's see if the sequence is Arithmetic :}$

$\textsf{If the difference between successive terms is }$ $\textsf{equal then, the terms are in AP}$

• $\textsf{-34 - (-29) = -5 }$

• $\textsf{-39 - (-34) = -5 }$

$\textsf{Since the common difference is same, }$ $\textsf{we can infer that it's an Arithmetic progression}$ $\textsf{with common difference of -5}$

Answer 2

Sequence: -29, -34, -39, -44, -49, ...

First we need to identify the terms:

• 1st term = -29

• 2nd term = -34

• 3rd term =  -39

• 4th term = -44

• 5th term  = -49

If the sequence is arithmetic, $\boxed{\sf \bold{second \ term = \dfrac{first \ term+third \ term}{2} }}$

If the sequence is geometric, $\boxed{\sf \bold{second \ term = \sqrt{first \ term \ x \ third \ term} }}$

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Check for arithmetic

$\rightarrow \sf -34 = \sf \dfrac{-29 +(-39)}{2}$

$\rightarrow \sf -34 = \sf \dfrac{-68}{2}$

$\rightarrow \sf -34 = -34$       [Hence it's arithmetic series]

To find common difference. we have to think of how to go to next term.

first term: -29

to go the second term, subtract by -5

-29 -5 = -34, second term

-34 - 5 = -39, third term

Hence, common difference: -5

Solutions:

Arithmetic Sequence

Common Difference: -5