সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=2.4$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {2.4}^{2-1}=30\cdot {2.4}^1=30\cdot 2.4=72$$

$$a_3=a_1·r^{n-1}=30\cdot {2.4}^{3-1}=30\cdot {2.4}^2=30\cdot 5.76=172.79999999999998$$

$$a_4=a_1·r^{n-1}=30\cdot {2.4}^{4-1}=30\cdot {2.4}^3=30\cdot 13.823999999999998=414.7199999999999$$

$$a_5=a_1·r^{n-1}=30\cdot {2.4}^{5-1}=30\cdot {2.4}^4=30\cdot 33.1776=995.328$$

$$a_6=a_1·r^{n-1}=30\cdot {2.4}^{6-1}=30\cdot {2.4}^5=30\cdot 79.62623999999998=2388.7871999999993$$

$$a_7=a_1·r^{n-1}=30\cdot {2.4}^{7-1}=30\cdot {2.4}^6=30\cdot 191.10297599999996=5733.089279999998$$

$$a_8=a_1·r^{n-1}=30\cdot {2.4}^{8-1}=30\cdot {2.4}^7=30\cdot 458.6471423999999=13759.414271999996$$

$$a_9=a_1·r^{n-1}=30\cdot {2.4}^{9-1}=30\cdot {2.4}^8=30\cdot 1100.7531417599996=33022.59425279999$$

$$a_{10}=a_1·r^{n-1}=30\cdot {2.4}^{10-1}=30\cdot {2.4}^9=30\cdot 2641.8075402239992=79254.22620671998$$