সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=3.5$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {3.5}^{2-1}=30\cdot {3.5}^1=30\cdot 3.5=105$$

$$a_3=a_1·r^{n-1}=30\cdot {3.5}^{3-1}=30\cdot {3.5}^2=30\cdot 12.25=367.5$$

$$a_4=a_1·r^{n-1}=30\cdot {3.5}^{4-1}=30\cdot {3.5}^3=30\cdot 42.875=1286.25$$

$$a_5=a_1·r^{n-1}=30\cdot {3.5}^{5-1}=30\cdot {3.5}^4=30\cdot 150.0625=4501.875$$

$$a_6=a_1·r^{n-1}=30\cdot {3.5}^{6-1}=30\cdot {3.5}^5=30\cdot 525.21875=15756.5625$$

$$a_7=a_1·r^{n-1}=30\cdot {3.5}^{7-1}=30\cdot {3.5}^6=30\cdot 1838.265625=55147.96875$$

$$a_8=a_1·r^{n-1}=30\cdot {3.5}^{8-1}=30\cdot {3.5}^7=30\cdot 6433.9296875=193017.890625$$

$$a_9=a_1·r^{n-1}=30\cdot {3.5}^{9-1}=30\cdot {3.5}^8=30\cdot 22518.75390625=675562.6171875$$

$$a_{10}=a_1·r^{n-1}=30\cdot {3.5}^{10-1}=30\cdot {3.5}^9=30\cdot 78815.638671875=2364469.16015625$$