সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=53$$ এবং সাধারণ অনুপাত: $$r=0.9245283018867925$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=53$$

$$a_2=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{2-1}=53\cdot {0.9245283018867925}^1=53\cdot 0.9245283018867925=49$$

$$a_3=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{3-1}=53\cdot {0.9245283018867925}^2=53\cdot 0.8547525809896761=45.301886792452834$$

$$a_4=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{4-1}=53\cdot {0.9245283018867925}^3=53\cdot 0.7902429522357383=41.882876468494125$$

$$a_5=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{5-1}=53\cdot {0.9245283018867925}^4=53\cdot 0.7306019747085127=38.72190465955118$$

$$a_6=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{6-1}=53\cdot {0.9245283018867925}^5=53\cdot 0.6754622030323986=35.799496760717126$$

$$a_7=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{7-1}=53\cdot {0.9245283018867925}^6=53\cdot 0.6244839235582553=33.097647948587536$$

$$a_8=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{8-1}=53\cdot {0.9245283018867925}^7=53\cdot 0.5773530614029153=30.59971225435451$$

$$a_9=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{9-1}=53\cdot {0.9245283018867925}^8=53\cdot 0.5337792454479783=28.29030000874285$$

$$a_{10}=a_1·r^{n-1}=53\cdot {0.9245283018867925}^{10-1}=53\cdot {0.9245283018867925}^9=53\cdot 0.4934940193764328=26.155183026950937$$