Question

I just need help with the equation for geometric and how to solve it along with the arithmetic equation as well. I already have question one which is the arithmetic sequence due to the constants of 200 if that's correct?

Answer 1

`\begin{gathered} 1)\text{ -38 , 162 , 362 , 562 , 762 , }\ldots\ldots.. \\ 162\text{ - (-38) = 200} \\ 362\text{ - 162 = 200} \\ 562\text{ - 362 = 200} \\ 762\text{ - 562 = 200} \\ As\text{ the difference betw}een\text{ the consecutive terms is constant. Thus the } \\ \text{given sequence is Arithmetic progression.} \\ 2)\text{ 2 , 8 , 32 , 128 , 512 , }\ldots\ldots \\ (8)/(2)=4 \\ (32)/(8)=4 \\ (128)/(32)=4 \\ (512)/(128)=4 \\ As\text{ the ratio betw}een\text{ the consecutive terms is constant. Thus the given } \\ \text{sequence is geometric progression.} \\ 3)\text{ 7 , }2\text{ , -3 , -8 , -13, }\ldots\ldots.. \\ 7\text{ - 2 = -5} \\ -3\text{ - 2 = -5} \\ -8\text{ - (-3) = -8 + 3 = -5} \\ -13\text{ - (-8) = -5} \\ As\text{ the diff}erence\text{ betw}een\text{ the consecutive terms is constant. Thus the} \\ \text{given sequence is Arithmetic Progression.} \\ 4)1,3^2,5^2,7^2,9^2,\ldots\ldots \\ \text{Neither the difference nor the ratio betw}een\text{ the consecutive terms is } \\ \text{constant .Thus the given sequence is neither Arithmetic nor Geometric } \\ \text{Progression.} \end{gathered}`