সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=65$$ এবং সাধারণ অনুপাত: $$r=2.4$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {2.4}^{2-1}=65\cdot {2.4}^1=65\cdot 2.4=156$$

$$a_3=a_1·r^{n-1}=65\cdot {2.4}^{3-1}=65\cdot {2.4}^2=65\cdot 5.76=374.4$$

$$a_4=a_1·r^{n-1}=65\cdot {2.4}^{4-1}=65\cdot {2.4}^3=65\cdot 13.823999999999998=898.5599999999998$$

$$a_5=a_1·r^{n-1}=65\cdot {2.4}^{5-1}=65\cdot {2.4}^4=65\cdot 33.1776=2156.544$$

$$a_6=a_1·r^{n-1}=65\cdot {2.4}^{6-1}=65\cdot {2.4}^5=65\cdot 79.62623999999998=5175.705599999998$$

$$a_7=a_1·r^{n-1}=65\cdot {2.4}^{7-1}=65\cdot {2.4}^6=65\cdot 191.10297599999996=12421.693439999997$$

$$a_8=a_1·r^{n-1}=65\cdot {2.4}^{8-1}=65\cdot {2.4}^7=65\cdot 458.6471423999999=29812.064255999994$$

$$a_9=a_1·r^{n-1}=65\cdot {2.4}^{9-1}=65\cdot {2.4}^8=65\cdot 1100.7531417599996=71548.95421439997$$

$$a_{10}=a_1·r^{n-1}=65\cdot {2.4}^{10-1}=65\cdot {2.4}^9=65\cdot 2641.8075402239992=171717.49011455994$$