সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=60$$ এবং সাধারণ অনুপাত: $$r=0.75$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=60$$

$$a_2=a_1·r^{n-1}=60\cdot {0.75}^{2-1}=60\cdot {0.75}^1=60\cdot 0.75=45$$

$$a_3=a_1·r^{n-1}=60\cdot {0.75}^{3-1}=60\cdot {0.75}^2=60\cdot 0.5625=33.75$$

$$a_4=a_1·r^{n-1}=60\cdot {0.75}^{4-1}=60\cdot {0.75}^3=60\cdot 0.421875=25.3125$$

$$a_5=a_1·r^{n-1}=60\cdot {0.75}^{5-1}=60\cdot {0.75}^4=60\cdot 0.31640625=18.984375$$

$$a_6=a_1·r^{n-1}=60\cdot {0.75}^{6-1}=60\cdot {0.75}^5=60\cdot 0.2373046875=14.23828125$$

$$a_7=a_1·r^{n-1}=60\cdot {0.75}^{7-1}=60\cdot {0.75}^6=60\cdot 0.177978515625=10.6787109375$$

$$a_8=a_1·r^{n-1}=60\cdot {0.75}^{8-1}=60\cdot {0.75}^7=60\cdot 0.13348388671875=8.009033203125$$

$$a_9=a_1·r^{n-1}=60\cdot {0.75}^{9-1}=60\cdot {0.75}^8=60\cdot 0.1001129150390625=6.00677490234375$$

$$a_{10}=a_1·r^{n-1}=60\cdot {0.75}^{10-1}=60\cdot {0.75}^9=60\cdot 0.07508468627929688=4.5050811767578125$$