সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=5$$ এবং সাধারণ অনুপাত: $$r=4.8$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=5$$

$$a_2=a_1·r^{n-1}=5\cdot {4.8}^{2-1}=5\cdot {4.8}^1=5\cdot 4.8=24$$

$$a_3=a_1·r^{n-1}=5\cdot {4.8}^{3-1}=5\cdot {4.8}^2=5\cdot 23.04=115.19999999999999$$

$$a_4=a_1·r^{n-1}=5\cdot {4.8}^{4-1}=5\cdot {4.8}^3=5\cdot 110.59199999999998=552.9599999999999$$

$$a_5=a_1·r^{n-1}=5\cdot {4.8}^{5-1}=5\cdot {4.8}^4=5\cdot 530.8416=2654.2079999999996$$

$$a_6=a_1·r^{n-1}=5\cdot {4.8}^{6-1}=5\cdot {4.8}^5=5\cdot 2548.0396799999994=12740.198399999997$$

$$a_7=a_1·r^{n-1}=5\cdot {4.8}^{7-1}=5\cdot {4.8}^6=5\cdot 12230.590463999997=61152.95231999998$$

$$a_8=a_1·r^{n-1}=5\cdot {4.8}^{8-1}=5\cdot {4.8}^7=5\cdot 58706.834227199986=293534.17113599996$$

$$a_9=a_1·r^{n-1}=5\cdot {4.8}^{9-1}=5\cdot {4.8}^8=5\cdot 281792.8042905599=1408964.0214527994$$

$$a_{10}=a_1·r^{n-1}=5\cdot {4.8}^{10-1}=5\cdot {4.8}^9=5\cdot 1352605.4605946876=6763027.302973438$$