সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=78$$ এবং সাধারণ অনুপাত: $$r=0.8461538461538461$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=78$$

$$a_2=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{2-1}=78\cdot {0.8461538461538461}^1=78\cdot 0.8461538461538461=66$$

$$a_3=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{3-1}=78\cdot {0.8461538461538461}^2=78\cdot 0.7159763313609467=55.84615384615385$$

$$a_4=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{4-1}=78\cdot {0.8461538461538461}^3=78\cdot 0.6058261265361857=47.25443786982249$$

$$a_5=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{5-1}=78\cdot {0.8461538461538461}^4=78\cdot 0.5126221070690802=39.98452435138825$$

$$a_6=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{6-1}=78\cdot {0.8461538461538461}^5=78\cdot 0.43375716751999094=33.833059066559294$$

$$a_7=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{7-1}=78\cdot {0.8461538461538461}^6=78\cdot 0.36702529559383845=28.627973056319398$$

$$a_8=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{8-1}=78\cdot {0.8461538461538461}^7=78\cdot 0.3105598655024787=24.22366950919334$$

$$a_9=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{9-1}=78\cdot {0.8461538461538461}^8=78\cdot 0.2627814246559435=20.496951123163594$$

$$a_{10}=a_1·r^{n-1}=78\cdot {0.8461538461538461}^{10-1}=78\cdot {0.8461538461538461}^9=78\cdot 0.22235351317041374=17.34357402729227$$