সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=72$$ এবং সাধারণ অনুপাত: $$r=0.75$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=72$$

$$a_2=a_1·r^{n-1}=72\cdot {0.75}^{2-1}=72\cdot {0.75}^1=72\cdot 0.75=54$$

$$a_3=a_1·r^{n-1}=72\cdot {0.75}^{3-1}=72\cdot {0.75}^2=72\cdot 0.5625=40.5$$

$$a_4=a_1·r^{n-1}=72\cdot {0.75}^{4-1}=72\cdot {0.75}^3=72\cdot 0.421875=30.375$$

$$a_5=a_1·r^{n-1}=72\cdot {0.75}^{5-1}=72\cdot {0.75}^4=72\cdot 0.31640625=22.78125$$

$$a_6=a_1·r^{n-1}=72\cdot {0.75}^{6-1}=72\cdot {0.75}^5=72\cdot 0.2373046875=17.0859375$$

$$a_7=a_1·r^{n-1}=72\cdot {0.75}^{7-1}=72\cdot {0.75}^6=72\cdot 0.177978515625=12.814453125$$

$$a_8=a_1·r^{n-1}=72\cdot {0.75}^{8-1}=72\cdot {0.75}^7=72\cdot 0.13348388671875=9.61083984375$$

$$a_9=a_1·r^{n-1}=72\cdot {0.75}^{9-1}=72\cdot {0.75}^8=72\cdot 0.1001129150390625=7.2081298828125$$

$$a_{10}=a_1·r^{n-1}=72\cdot {0.75}^{10-1}=72\cdot {0.75}^9=72\cdot 0.07508468627929688=5.406097412109375$$