সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=13$$ এবং সাধারণ অনুপাত: $$r=1.1538461538461537$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=13$$

$$a_2=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{2-1}=13\cdot {1.1538461538461537}^1=13\cdot 1.1538461538461537=14.999999999999998$$

$$a_3=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{3-1}=13\cdot {1.1538461538461537}^2=13\cdot 1.3313609467455618=17.307692307692303$$

$$a_4=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{4-1}=13\cdot {1.1538461538461537}^3=13\cdot 1.5361857077833405=19.970414201183427$$

$$a_5=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{5-1}=13\cdot {1.1538461538461537}^4=13\cdot 1.772521970519239=23.042785616750106$$

$$a_6=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{6-1}=13\cdot {1.1538461538461537}^5=13\cdot 2.0452176582914294=26.58782955778858$$

$$a_7=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{7-1}=13\cdot {1.1538461538461537}^6=13\cdot 2.3598665287978027=30.678264874371436$$

$$a_8=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{8-1}=13\cdot {1.1538461538461537}^7=13\cdot 2.7229229178436185=35.39799793196704$$

$$a_9=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{9-1}=13\cdot {1.1538461538461537}^8=13\cdot 3.1418341359734057=40.84384376765427$$

$$a_{10}=a_1·r^{n-1}=13\cdot {1.1538461538461537}^{10-1}=13\cdot {1.1538461538461537}^9=13\cdot 3.6251932338154678=47.12751203960108$$