সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=32$$ এবং সাধারণ অনুপাত: $$r=0.75$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=32$$

$$a_2=a_1·r^{n-1}=32\cdot {0.75}^{2-1}=32\cdot {0.75}^1=32\cdot 0.75=24$$

$$a_3=a_1·r^{n-1}=32\cdot {0.75}^{3-1}=32\cdot {0.75}^2=32\cdot 0.5625=18$$

$$a_4=a_1·r^{n-1}=32\cdot {0.75}^{4-1}=32\cdot {0.75}^3=32\cdot 0.421875=13.5$$

$$a_5=a_1·r^{n-1}=32\cdot {0.75}^{5-1}=32\cdot {0.75}^4=32\cdot 0.31640625=10.125$$

$$a_6=a_1·r^{n-1}=32\cdot {0.75}^{6-1}=32\cdot {0.75}^5=32\cdot 0.2373046875=7.59375$$

$$a_7=a_1·r^{n-1}=32\cdot {0.75}^{7-1}=32\cdot {0.75}^6=32\cdot 0.177978515625=5.6953125$$

$$a_8=a_1·r^{n-1}=32\cdot {0.75}^{8-1}=32\cdot {0.75}^7=32\cdot 0.13348388671875=4.271484375$$

$$a_9=a_1·r^{n-1}=32\cdot {0.75}^{9-1}=32\cdot {0.75}^8=32\cdot 0.1001129150390625=3.20361328125$$

$$a_{10}=a_1·r^{n-1}=32\cdot {0.75}^{10-1}=32\cdot {0.75}^9=32\cdot 0.07508468627929688=2.4027099609375$$