সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=53$$ এবং সাধারণ অনুপাত: $$r=0.7924528301886793$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=53$$

$$a_2=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{2-1}=53\cdot {0.7924528301886793}^1=53\cdot 0.7924528301886793=42$$

$$a_3=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{3-1}=53\cdot {0.7924528301886793}^2=53\cdot 0.6279814880740477=33.28301886792453$$

$$a_4=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{4-1}=53\cdot {0.7924528301886793}^3=53\cdot 0.4976457075303775=26.37522249911001$$

$$a_5=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{5-1}=53\cdot {0.7924528301886793}^4=53\cdot 0.3943607493636954=20.901119716275858$$

$$a_6=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{6-1}=53\cdot {0.7924528301886793}^5=53\cdot 0.3125122919485888=16.56315147327521$$

$$a_7=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{7-1}=53\cdot {0.7924528301886793}^6=53\cdot 0.24765125022341003=13.125516261840732$$

$$a_8=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{8-1}=53\cdot {0.7924528301886793}^7=53\cdot 0.19625193413930608=10.401352509383223$$

$$a_9=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{9-1}=53\cdot {0.7924528301886793}^8=53\cdot 0.15552040063869538=8.242581233850855$$

$$a_{10}=a_1·r^{n-1}=53\cdot {0.7924528301886793}^{10-1}=53\cdot {0.7924528301886793}^9=53\cdot 0.12324258163821145=6.531856826825207$$