সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=15$$ এবং সাধারণ অনুপাত: $$r=1.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=15$$

$$a_2=a_1·r^{n-1}=15\cdot {1.8}^{2-1}=15\cdot {1.8}^1=15\cdot 1.8=27$$

$$a_3=a_1·r^{n-1}=15\cdot {1.8}^{3-1}=15\cdot {1.8}^2=15\cdot 3.24=48.6$$

$$a_4=a_1·r^{n-1}=15\cdot {1.8}^{4-1}=15\cdot {1.8}^3=15\cdot 5.832000000000001=87.48000000000002$$

$$a_5=a_1·r^{n-1}=15\cdot {1.8}^{5-1}=15\cdot {1.8}^4=15\cdot 10.4976=157.464$$

$$a_6=a_1·r^{n-1}=15\cdot {1.8}^{6-1}=15\cdot {1.8}^5=15\cdot 18.895680000000002=283.4352$$

$$a_7=a_1·r^{n-1}=15\cdot {1.8}^{7-1}=15\cdot {1.8}^6=15\cdot 34.012224=510.18336000000005$$

$$a_8=a_1·r^{n-1}=15\cdot {1.8}^{8-1}=15\cdot {1.8}^7=15\cdot 61.22200320000001=918.3300480000001$$

$$a_9=a_1·r^{n-1}=15\cdot {1.8}^{9-1}=15\cdot {1.8}^8=15\cdot 110.19960576000003=1652.9940864000005$$

$$a_{10}=a_1·r^{n-1}=15\cdot {1.8}^{10-1}=15\cdot {1.8}^9=15\cdot 198.35929036800005=2975.3893555200007$$