সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=125$$ এবং সাধারণ অনুপাত: $$r=1.72$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=125$$

$$a_2=a_1·r^{n-1}=125\cdot {1.72}^{2-1}=125\cdot {1.72}^1=125\cdot 1.72=215$$

$$a_3=a_1·r^{n-1}=125\cdot {1.72}^{3-1}=125\cdot {1.72}^2=125\cdot 2.9583999999999997=369.79999999999995$$

$$a_4=a_1·r^{n-1}=125\cdot {1.72}^{4-1}=125\cdot {1.72}^3=125\cdot 5.088448=636.0559999999999$$

$$a_5=a_1·r^{n-1}=125\cdot {1.72}^{5-1}=125\cdot {1.72}^4=125\cdot 8.75213056=1094.01632$$

$$a_6=a_1·r^{n-1}=125\cdot {1.72}^{6-1}=125\cdot {1.72}^5=125\cdot 15.053664563199998=1881.7080703999998$$

$$a_7=a_1·r^{n-1}=125\cdot {1.72}^{7-1}=125\cdot {1.72}^6=125\cdot 25.892303048703997=3236.5378810879997$$

$$a_8=a_1·r^{n-1}=125\cdot {1.72}^{8-1}=125\cdot {1.72}^7=125\cdot 44.53476124377087=5566.845155471359$$

$$a_9=a_1·r^{n-1}=125\cdot {1.72}^{9-1}=125\cdot {1.72}^8=125\cdot 76.5997893392859=9574.973667410739$$

$$a_{10}=a_1·r^{n-1}=125\cdot {1.72}^{10-1}=125\cdot {1.72}^9=125\cdot 131.75163766357176=16468.95470794647$$