সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=5.5$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {5.5}^{2-1}=30\cdot {5.5}^1=30\cdot 5.5=165$$

$$a_3=a_1·r^{n-1}=30\cdot {5.5}^{3-1}=30\cdot {5.5}^2=30\cdot 30.25=907.5$$

$$a_4=a_1·r^{n-1}=30\cdot {5.5}^{4-1}=30\cdot {5.5}^3=30\cdot 166.375=4991.25$$

$$a_5=a_1·r^{n-1}=30\cdot {5.5}^{5-1}=30\cdot {5.5}^4=30\cdot 915.0625=27451.875$$

$$a_6=a_1·r^{n-1}=30\cdot {5.5}^{6-1}=30\cdot {5.5}^5=30\cdot 5032.84375=150985.3125$$

$$a_7=a_1·r^{n-1}=30\cdot {5.5}^{7-1}=30\cdot {5.5}^6=30\cdot 27680.640625=830419.21875$$

$$a_8=a_1·r^{n-1}=30\cdot {5.5}^{8-1}=30\cdot {5.5}^7=30\cdot 152243.5234375=4567305.703125$$

$$a_9=a_1·r^{n-1}=30\cdot {5.5}^{9-1}=30\cdot {5.5}^8=30\cdot 837339.37890625=25120181.3671875$$

$$a_{10}=a_1·r^{n-1}=30\cdot {5.5}^{10-1}=30\cdot {5.5}^9=30\cdot 4605366.583984375=138160997.51953125$$