সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=150$$ এবং সাধারণ অনুপাত: $$r=1.4$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=150$$

$$a_2=a_1·r^{n-1}=150\cdot {1.4}^{2-1}=150\cdot {1.4}^1=150\cdot 1.4=210$$

$$a_3=a_1·r^{n-1}=150\cdot {1.4}^{3-1}=150\cdot {1.4}^2=150\cdot 1.9599999999999997=293.99999999999994$$

$$a_4=a_1·r^{n-1}=150\cdot {1.4}^{4-1}=150\cdot {1.4}^3=150\cdot 2.7439999999999993=411.5999999999999$$

$$a_5=a_1·r^{n-1}=150\cdot {1.4}^{5-1}=150\cdot {1.4}^4=150\cdot 3.8415999999999992=576.2399999999999$$

$$a_6=a_1·r^{n-1}=150\cdot {1.4}^{6-1}=150\cdot {1.4}^5=150\cdot 5.378239999999998=806.7359999999998$$

$$a_7=a_1·r^{n-1}=150\cdot {1.4}^{7-1}=150\cdot {1.4}^6=150\cdot 7.529535999999998=1129.4303999999997$$

$$a_8=a_1·r^{n-1}=150\cdot {1.4}^{8-1}=150\cdot {1.4}^7=150\cdot 10.541350399999995=1581.2025599999993$$

$$a_9=a_1·r^{n-1}=150\cdot {1.4}^{9-1}=150\cdot {1.4}^8=150\cdot 14.757890559999993=2213.683583999999$$

$$a_{10}=a_1·r^{n-1}=150\cdot {1.4}^{10-1}=150\cdot {1.4}^9=150\cdot 20.66104678399999=3099.157017599998$$