সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=0.44$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {0.44}^{2-1}=75\cdot {0.44}^1=75\cdot 0.44=33$$

$$a_3=a_1·r^{n-1}=75\cdot {0.44}^{3-1}=75\cdot {0.44}^2=75\cdot 0.1936=14.52$$

$$a_4=a_1·r^{n-1}=75\cdot {0.44}^{4-1}=75\cdot {0.44}^3=75\cdot 0.085184=6.3888$$

$$a_5=a_1·r^{n-1}=75\cdot {0.44}^{5-1}=75\cdot {0.44}^4=75\cdot 0.03748096=2.8110720000000002$$

$$a_6=a_1·r^{n-1}=75\cdot {0.44}^{6-1}=75\cdot {0.44}^5=75\cdot 0.0164916224=1.23687168$$

$$a_7=a_1·r^{n-1}=75\cdot {0.44}^{7-1}=75\cdot {0.44}^6=75\cdot 0.007256313856=0.5442235392$$

$$a_8=a_1·r^{n-1}=75\cdot {0.44}^{8-1}=75\cdot {0.44}^7=75\cdot 0.00319277809664=0.23945835724800002$$

$$a_9=a_1·r^{n-1}=75\cdot {0.44}^{9-1}=75\cdot {0.44}^8=75\cdot 0.0014048223625216=0.10536167718912$$

$$a_{10}=a_1·r^{n-1}=75\cdot {0.44}^{10-1}=75\cdot {0.44}^9=75\cdot 0.000618121839509504=0.0463591379632128$$