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.
1, 3, 6, 10, 15, …
My answer below:
3 + 1 = 4
3 - 6 = -3
so, I get neither?

Answer 1

Sequence: 1, 3, 6, 10, 15, …

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

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

Check for arithmetic:

$\sf \rightarrow 3 = \dfrac{1+6}{2}$

$\sf \rightarrow 3 =3.5$    Hence, the sequence is not arithmetic

Check for geometric:

$\sf \rightarrow 3 = \sqrt{1*6}$

$\sf \rightarrow 3 = \sqrt{6}$   Hence, the sequence is not geometric

Solution:

• Neither

Answer 2

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

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

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

$\textsf{and}$

• $\textsf{If the ratio of successive terms is }$ $\textsf{equal then, the terms are in GP}$

$\textsf{Since neither common difference is same, }$ $\textsf{nor common ratio is same, therefore }$ $\textsf{we can infer that it's neither an Arithmetic progression}$ $\textsf{nor Geometric progression. }$

Hope it helps ~