সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=2.7$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {2.7}^{2-1}=30\cdot {2.7}^1=30\cdot 2.7=81$$

$$a_3=a_1·r^{n-1}=30\cdot {2.7}^{3-1}=30\cdot {2.7}^2=30\cdot 7.290000000000001=218.70000000000002$$

$$a_4=a_1·r^{n-1}=30\cdot {2.7}^{4-1}=30\cdot {2.7}^3=30\cdot 19.683000000000003=590.4900000000001$$

$$a_5=a_1·r^{n-1}=30\cdot {2.7}^{5-1}=30\cdot {2.7}^4=30\cdot 53.144100000000016=1594.3230000000005$$

$$a_6=a_1·r^{n-1}=30\cdot {2.7}^{6-1}=30\cdot {2.7}^5=30\cdot 143.48907000000005=4304.672100000002$$

$$a_7=a_1·r^{n-1}=30\cdot {2.7}^{7-1}=30\cdot {2.7}^6=30\cdot 387.42048900000015=11622.614670000004$$

$$a_8=a_1·r^{n-1}=30\cdot {2.7}^{8-1}=30\cdot {2.7}^7=30\cdot 1046.0353203000004=31381.05960900001$$

$$a_9=a_1·r^{n-1}=30\cdot {2.7}^{9-1}=30\cdot {2.7}^8=30\cdot 2824.2953648100015=84728.86094430005$$

$$a_{10}=a_1·r^{n-1}=30\cdot {2.7}^{10-1}=30\cdot {2.7}^9=30\cdot 7625.5974849870045=228767.92454961012$$