সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=4.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {4.8}^{2-1}=75\cdot {4.8}^1=75\cdot 4.8=360$$

$$a_3=a_1·r^{n-1}=75\cdot {4.8}^{3-1}=75\cdot {4.8}^2=75\cdot 23.04=1728$$

$$a_4=a_1·r^{n-1}=75\cdot {4.8}^{4-1}=75\cdot {4.8}^3=75\cdot 110.59199999999998=8294.4$$

$$a_5=a_1·r^{n-1}=75\cdot {4.8}^{5-1}=75\cdot {4.8}^4=75\cdot 530.8416=39813.119999999995$$

$$a_6=a_1·r^{n-1}=75\cdot {4.8}^{6-1}=75\cdot {4.8}^5=75\cdot 2548.0396799999994=191102.97599999997$$

$$a_7=a_1·r^{n-1}=75\cdot {4.8}^{7-1}=75\cdot {4.8}^6=75\cdot 12230.590463999997=917294.2847999998$$

$$a_8=a_1·r^{n-1}=75\cdot {4.8}^{8-1}=75\cdot {4.8}^7=75\cdot 58706.834227199986=4403012.567039999$$

$$a_9=a_1·r^{n-1}=75\cdot {4.8}^{9-1}=75\cdot {4.8}^8=75\cdot 281792.8042905599=21134460.32179199$$

$$a_{10}=a_1·r^{n-1}=75\cdot {4.8}^{10-1}=75\cdot {4.8}^9=75\cdot 1352605.4605946876=101445409.54460157$$