সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=30$$ এবং সাধারণ অনুপাত: $$r=0.7$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=30$$

$$a_2=a_1·r^{n-1}=30\cdot {0.7}^{2-1}=30\cdot {0.7}^1=30\cdot 0.7=21$$

$$a_3=a_1·r^{n-1}=30\cdot {0.7}^{3-1}=30\cdot {0.7}^2=30\cdot 0.48999999999999994=14.699999999999998$$

$$a_4=a_1·r^{n-1}=30\cdot {0.7}^{4-1}=30\cdot {0.7}^3=30\cdot 0.3429999999999999=10.289999999999997$$

$$a_5=a_1·r^{n-1}=30\cdot {0.7}^{5-1}=30\cdot {0.7}^4=30\cdot 0.24009999999999995=7.2029999999999985$$

$$a_6=a_1·r^{n-1}=30\cdot {0.7}^{6-1}=30\cdot {0.7}^5=30\cdot 0.16806999999999994=5.042099999999998$$

$$a_7=a_1·r^{n-1}=30\cdot {0.7}^{7-1}=30\cdot {0.7}^6=30\cdot 0.11764899999999996=3.529469999999999$$

$$a_8=a_1·r^{n-1}=30\cdot {0.7}^{8-1}=30\cdot {0.7}^7=30\cdot 0.08235429999999996=2.470628999999999$$

$$a_9=a_1·r^{n-1}=30\cdot {0.7}^{9-1}=30\cdot {0.7}^8=30\cdot 0.05764800999999997=1.7294402999999992$$

$$a_{10}=a_1·r^{n-1}=30\cdot {0.7}^{10-1}=30\cdot {0.7}^9=30\cdot 0.04035360699999998=1.2106082099999993$$