Answer:
3) 18, 5.5, –7, –19.5, –32, … sequence is in Arithmetic Progression.
5) 16, 32, 48, 64, 80 sequence is in Arithmetic Progression.
Step-by-step explanation:
If, a, b, c ,k, e ... is a given sequence.
Then the above sequence is in AP if b - a = c - b = k - c = ...
or, each term has same COMMON DIFFERENCE (d).
Here, take each sequence and check for the value of d.
1) –5, 5, –5, 5, –5, …
Here, 5 - (-5) = 10, -5 - 5 = -10
and 10 ≠ -10. So the sequence is NOT in Arithmetic Progression.
2)96, 48, 24, 12, 6
Here, 48 - 96 = -48, 24 - 48 = -24
and -48 ≠ -24. So the sequence is NOT in Arithmetic Progression.
3)18, 5.5, –7, –19.5, –32, …
Here, 5.5 - 18 = -12.5 , -7 - 5.5 = -12.5 ..
and -12.5 is the common difference.
So the sequence is in Arithmetic Progression.
4)–1, –3, –9, –27, –81, …
Here, -3-(-1) = - 2 -9 - (-3) = -6
and -2 ≠ -6. So the sequence is NOT in Arithmetic Progression.
5)16, 32, 48, 64, 80
Here, 32 - 16 = 16 , 48 - 32= 16 ..
and 16 is the common difference.
So the sequence is in Arithmetic Progression.
![\sqrt[4]{ x^{3} } = x^{3/4}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B%20x%5E%7B3%7D%20%7D%20%3D%20x%5E%7B3%2F4%7D%20)
![\sqrt[10]{ x^{5} * x^{4}* x^{2} } = \sqrt[10]{ x^{11} }= x^{11/10}](https://tex.z-dn.net/?f=%20%5Csqrt%5B10%5D%7B%20x%5E%7B5%7D%20%2A%20x%5E%7B4%7D%2A%20x%5E%7B2%7D%20%20%7D%20%3D%20%5Csqrt%5B10%5D%7B%20x%5E%7B11%7D%20%7D%3D%20x%5E%7B11%2F10%7D%20%20)
