সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=32$$ এবং সাধারণ অনুপাত: $$r=0.84375$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=32$$

$$a_2=a_1·r^{n-1}=32\cdot {0.84375}^{2-1}=32\cdot {0.84375}^1=32\cdot 0.84375=27$$

$$a_3=a_1·r^{n-1}=32\cdot {0.84375}^{3-1}=32\cdot {0.84375}^2=32\cdot 0.7119140625=22.78125$$

$$a_4=a_1·r^{n-1}=32\cdot {0.84375}^{4-1}=32\cdot {0.84375}^3=32\cdot 0.600677490234375=19.2216796875$$

$$a_5=a_1·r^{n-1}=32\cdot {0.84375}^{5-1}=32\cdot {0.84375}^4=32\cdot 0.5068216323852539=16.218292236328125$$

$$a_6=a_1·r^{n-1}=32\cdot {0.84375}^{6-1}=32\cdot {0.84375}^5=32\cdot 0.427630752325058=13.684184074401855$$

$$a_7=a_1·r^{n-1}=32\cdot {0.84375}^{7-1}=32\cdot {0.84375}^6=32\cdot 0.3608134472742677=11.546030312776566$$

$$a_8=a_1·r^{n-1}=32\cdot {0.84375}^{8-1}=32\cdot {0.84375}^7=32\cdot 0.30443634613766335=9.741963076405227$$

$$a_9=a_1·r^{n-1}=32\cdot {0.84375}^{9-1}=32\cdot {0.84375}^8=32\cdot 0.25686816705365345=8.21978134571691$$

$$a_{10}=a_1·r^{n-1}=32\cdot {0.84375}^{10-1}=32\cdot {0.84375}^9=32\cdot 0.2167325159515201=6.935440510448643$$