সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=125$$ এবং সাধারণ অনুপাত: $$r=1.6$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=125$$

$$a_2=a_1·r^{n-1}=125\cdot {1.6}^{2-1}=125\cdot {1.6}^1=125\cdot 1.6=200$$

$$a_3=a_1·r^{n-1}=125\cdot {1.6}^{3-1}=125\cdot {1.6}^2=125\cdot 2.5600000000000005=320.00000000000006$$

$$a_4=a_1·r^{n-1}=125\cdot {1.6}^{4-1}=125\cdot {1.6}^3=125\cdot 4.096000000000001=512.0000000000001$$

$$a_5=a_1·r^{n-1}=125\cdot {1.6}^{5-1}=125\cdot {1.6}^4=125\cdot 6.553600000000001=819.2000000000002$$

$$a_6=a_1·r^{n-1}=125\cdot {1.6}^{6-1}=125\cdot {1.6}^5=125\cdot 10.485760000000003=1310.7200000000003$$

$$a_7=a_1·r^{n-1}=125\cdot {1.6}^{7-1}=125\cdot {1.6}^6=125\cdot 16.777216000000006=2097.152000000001$$

$$a_8=a_1·r^{n-1}=125\cdot {1.6}^{8-1}=125\cdot {1.6}^7=125\cdot 26.84354560000001=3355.443200000001$$

$$a_9=a_1·r^{n-1}=125\cdot {1.6}^{9-1}=125\cdot {1.6}^8=125\cdot 42.94967296000002=5368.709120000003$$

$$a_{10}=a_1·r^{n-1}=125\cdot {1.6}^{10-1}=125\cdot {1.6}^9=125\cdot 68.71947673600003=8589.934592000003$$