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

`\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 ~

Answer 2

Sequence: 1, 3, 6, 10, 15, …

If sequence is arithmetic,
`\boxed{\sf \bold{second \ term = (first \ term+third \ term)/(2) }}`

If sequence is geometric,
`\boxed{\sf \bold{second \ term = √(first \ term \ * \ third \ term) }}`

Check for arithmetic:

`\sf \rightarrow 3 = (1+6)/(2)`

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

Check for geometric:

`\sf \rightarrow 3 = √(1*6)`

`\sf \rightarrow 3 = √(6)` Hence, the sequence is not geometric

Solution:

• Neither