সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=123$$ এবং সাধারণ অনুপাত: $$r=2.252032520325203$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=123$$

$$a_2=a_1·r^{n-1}=123\cdot {2.252032520325203}^{2-1}=123\cdot {2.252032520325203}^1=123\cdot 2.252032520325203=277$$

$$a_3=a_1·r^{n-1}=123\cdot {2.252032520325203}^{3-1}=123\cdot {2.252032520325203}^2=123\cdot 5.071650472602287=623.8130081300814$$

$$a_4=a_1·r^{n-1}=123\cdot {2.252032520325203}^{4-1}=123\cdot {2.252032520325203}^3=123\cdot 11.421521796023036=1404.8471809108335$$

$$a_5=a_1·r^{n-1}=123\cdot {2.252032520325203}^{5-1}=123\cdot {2.252032520325203}^4=123\cdot 25.721638516246998=3163.7615374983807$$

$$a_6=a_1·r^{n-1}=123\cdot {2.252032520325203}^{6-1}=123\cdot {2.252032520325203}^5=123\cdot 57.92596641463754=7124.893869000418$$

$$a_7=a_1·r^{n-1}=123\cdot {2.252032520325203}^{7-1}=123\cdot {2.252032520325203}^6=123\cdot 130.45116013702926=16045.492696854599$$

$$a_8=a_1·r^{n-1}=123\cdot {2.252032520325203}^{8-1}=123\cdot {2.252032520325203}^7=123\cdot 293.78025494274067=36134.9713579571$$

$$a_9=a_1·r^{n-1}=123\cdot {2.252032520325203}^{9-1}=123\cdot {2.252032520325203}^8=123\cdot 661.602687960481=81377.13061913916$$

$$a_{10}=a_1·r^{n-1}=123\cdot {2.252032520325203}^{10-1}=123\cdot {2.252032520325203}^9=123\cdot 1489.950768821571=183263.94456505324$$