সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=-39$$ এবং সাধারণ অনুপাত: $$r=1.6153846153846154$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=-39$$

$$a_2=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{2-1}=-39\cdot {1.6153846153846154}^1=-39\cdot 1.6153846153846154=-63$$

$$a_3=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{3-1}=-39\cdot {1.6153846153846154}^2=-39\cdot 2.609467455621302=-101.76923076923077$$

$$a_4=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{4-1}=-39\cdot {1.6153846153846154}^3=-39\cdot 4.2152935821574875=-164.39644970414201$$

$$a_5=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{5-1}=-39\cdot {1.6153846153846154}^4=-39\cdot 6.809320401946711=-265.56349567592173$$

$$a_6=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{6-1}=-39\cdot {1.6153846153846154}^5=-39\cdot 10.999671418529303=-428.9871853226428$$

$$a_7=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{7-1}=-39\cdot {1.6153846153846154}^6=-39\cdot 17.768699983778106=-692.9792993673461$$

$$a_8=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{8-1}=-39\cdot {1.6153846153846154}^7=-39\cdot 28.703284589180015=-1119.4280989780207$$

$$a_9=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{9-1}=-39\cdot {1.6153846153846154}^8=-39\cdot 46.36684433636772=-1808.306929118341$$

$$a_{10}=a_1·r^{n-1}=-39\cdot {1.6153846153846154}^{10-1}=-39\cdot {1.6153846153846154}^9=-39\cdot 74.9002870049017=-2921.1111931911664$$