Answer:
10th term of the sequence = 0.537
Step-by-step explanation:
First three terms of the sequence are → 5, 4,
..........
Ratio of 2nd and 1st term of the sequence = ![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
Ratio of 3rd and 2nd term of the sequence = ![\frac{\frac{16}{5} }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B16%7D%7B5%7D%20%7D%7B4%7D)
= ![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
Therefore, ratio between every successive term to the previous term is common.
Common ratio 'r' = ![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
First term of the sequence 'a' = 5
nth term of a geometric sequence = ![a(r)^n](https://tex.z-dn.net/?f=a%28r%29%5En)
Therefore, nth term of the given term will be ![T_n=5(\frac{4}{5})^n](https://tex.z-dn.net/?f=T_n%3D5%28%5Cfrac%7B4%7D%7B5%7D%29%5En)
Now we have to find the 10 term of the given sequence.
For n = 10,
![T_{10}=5(\frac{4}{5})^{10}](https://tex.z-dn.net/?f=T_%7B10%7D%3D5%28%5Cfrac%7B4%7D%7B5%7D%29%5E%7B10%7D)
= 0.53687
≈ 0.537
Therefore, 10th term of the sequence is 0.537
Answer:
n= 15cm
Step-by-step explanation:
9 squared + 12 squared = N
Hope this helps!