সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=32$$ এবং সাধারণ অনুপাত: $$r=1.90625$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=32$$

$$a_2=a_1·r^{n-1}=32\cdot {1.90625}^{2-1}=32\cdot {1.90625}^1=32\cdot 1.90625=61$$

$$a_3=a_1·r^{n-1}=32\cdot {1.90625}^{3-1}=32\cdot {1.90625}^2=32\cdot 3.6337890625=116.28125$$

$$a_4=a_1·r^{n-1}=32\cdot {1.90625}^{4-1}=32\cdot {1.90625}^3=32\cdot 6.926910400390625=221.6611328125$$

$$a_5=a_1·r^{n-1}=32\cdot {1.90625}^{5-1}=32\cdot {1.90625}^4=32\cdot 13.204422950744629=422.5415344238281$$

$$a_6=a_1·r^{n-1}=32\cdot {1.90625}^{6-1}=32\cdot {1.90625}^5=32\cdot 25.17093124985695=805.4697999954224$$

$$a_7=a_1·r^{n-1}=32\cdot {1.90625}^{7-1}=32\cdot {1.90625}^6=32\cdot 47.98208769503981=1535.4268062412739$$

$$a_8=a_1·r^{n-1}=32\cdot {1.90625}^{8-1}=32\cdot {1.90625}^7=32\cdot 91.46585466866964=2926.9073493974283$$

$$a_9=a_1·r^{n-1}=32\cdot {1.90625}^{9-1}=32\cdot {1.90625}^8=32\cdot 174.3567854621515=5579.417134788848$$

$$a_{10}=a_1·r^{n-1}=32\cdot {1.90625}^{10-1}=32\cdot {1.90625}^9=32\cdot 332.36762228722625=10635.76391319124$$