সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=105$$ এবং সাধারণ অনুপাত: $$r=1.4$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=105$$

$$a_2=a_1·r^{n-1}=105\cdot {1.4}^{2-1}=105\cdot {1.4}^1=105\cdot 1.4=147$$

$$a_3=a_1·r^{n-1}=105\cdot {1.4}^{3-1}=105\cdot {1.4}^2=105\cdot 1.9599999999999997=205.79999999999998$$

$$a_4=a_1·r^{n-1}=105\cdot {1.4}^{4-1}=105\cdot {1.4}^3=105\cdot 2.7439999999999993=288.11999999999995$$

$$a_5=a_1·r^{n-1}=105\cdot {1.4}^{5-1}=105\cdot {1.4}^4=105\cdot 3.8415999999999992=403.36799999999994$$

$$a_6=a_1·r^{n-1}=105\cdot {1.4}^{6-1}=105\cdot {1.4}^5=105\cdot 5.378239999999998=564.7151999999998$$

$$a_7=a_1·r^{n-1}=105\cdot {1.4}^{7-1}=105\cdot {1.4}^6=105\cdot 7.529535999999998=790.6012799999997$$

$$a_8=a_1·r^{n-1}=105\cdot {1.4}^{8-1}=105\cdot {1.4}^7=105\cdot 10.541350399999995=1106.8417919999995$$

$$a_9=a_1·r^{n-1}=105\cdot {1.4}^{9-1}=105\cdot {1.4}^8=105\cdot 14.757890559999993=1549.5785087999993$$

$$a_{10}=a_1·r^{n-1}=105\cdot {1.4}^{10-1}=105\cdot {1.4}^9=105\cdot 20.66104678399999=2169.409912319999$$