সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=1.96$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {1.96}^{2-1}=75\cdot {1.96}^1=75\cdot 1.96=147$$

$$a_3=a_1·r^{n-1}=75\cdot {1.96}^{3-1}=75\cdot {1.96}^2=75\cdot 3.8415999999999997=288.12$$

$$a_4=a_1·r^{n-1}=75\cdot {1.96}^{4-1}=75\cdot {1.96}^3=75\cdot 7.529535999999999=564.7152$$

$$a_5=a_1·r^{n-1}=75\cdot {1.96}^{5-1}=75\cdot {1.96}^4=75\cdot 14.757890559999998=1106.841792$$

$$a_6=a_1·r^{n-1}=75\cdot {1.96}^{6-1}=75\cdot {1.96}^5=75\cdot 28.925465497599998=2169.40991232$$

$$a_7=a_1·r^{n-1}=75\cdot {1.96}^{7-1}=75\cdot {1.96}^6=75\cdot 56.693912375295994=4252.0434281472$$

$$a_8=a_1·r^{n-1}=75\cdot {1.96}^{8-1}=75\cdot {1.96}^7=75\cdot 111.12006825558015=8334.00511916851$$

$$a_9=a_1·r^{n-1}=75\cdot {1.96}^{9-1}=75\cdot {1.96}^8=75\cdot 217.79533378093709=16334.650033570282$$

$$a_{10}=a_1·r^{n-1}=75\cdot {1.96}^{10-1}=75\cdot {1.96}^9=75\cdot 426.8788542106367=32015.91406579775$$