সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=64$$ এবং সাধারণ অনুপাত: $$r=1.25$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {1.25}^{2-1}=64\cdot {1.25}^1=64\cdot 1.25=80$$

$$a_3=a_1·r^{n-1}=64\cdot {1.25}^{3-1}=64\cdot {1.25}^2=64\cdot 1.5625=100$$

$$a_4=a_1·r^{n-1}=64\cdot {1.25}^{4-1}=64\cdot {1.25}^3=64\cdot 1.953125=125$$

$$a_5=a_1·r^{n-1}=64\cdot {1.25}^{5-1}=64\cdot {1.25}^4=64\cdot 2.44140625=156.25$$

$$a_6=a_1·r^{n-1}=64\cdot {1.25}^{6-1}=64\cdot {1.25}^5=64\cdot 3.0517578125=195.3125$$

$$a_7=a_1·r^{n-1}=64\cdot {1.25}^{7-1}=64\cdot {1.25}^6=64\cdot 3.814697265625=244.140625$$

$$a_8=a_1·r^{n-1}=64\cdot {1.25}^{8-1}=64\cdot {1.25}^7=64\cdot 4.76837158203125=305.17578125$$

$$a_9=a_1·r^{n-1}=64\cdot {1.25}^{9-1}=64\cdot {1.25}^8=64\cdot 5.9604644775390625=381.4697265625$$

$$a_{10}=a_1·r^{n-1}=64\cdot {1.25}^{10-1}=64\cdot {1.25}^9=64\cdot 7.450580596923828=476.837158203125$$