সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=1.44$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {1.44}^{2-1}=75\cdot {1.44}^1=75\cdot 1.44=108$$

$$a_3=a_1·r^{n-1}=75\cdot {1.44}^{3-1}=75\cdot {1.44}^2=75\cdot 2.0736=155.51999999999998$$

$$a_4=a_1·r^{n-1}=75\cdot {1.44}^{4-1}=75\cdot {1.44}^3=75\cdot 2.9859839999999997=223.94879999999998$$

$$a_5=a_1·r^{n-1}=75\cdot {1.44}^{5-1}=75\cdot {1.44}^4=75\cdot 4.299816959999999=322.48627199999993$$

$$a_6=a_1·r^{n-1}=75\cdot {1.44}^{6-1}=75\cdot {1.44}^5=75\cdot 6.191736422399999=464.38023167999995$$

$$a_7=a_1·r^{n-1}=75\cdot {1.44}^{7-1}=75\cdot {1.44}^6=75\cdot 8.916100448255998=668.7075336191998$$

$$a_8=a_1·r^{n-1}=75\cdot {1.44}^{8-1}=75\cdot {1.44}^7=75\cdot 12.839184645488636=962.9388484116478$$

$$a_9=a_1·r^{n-1}=75\cdot {1.44}^{9-1}=75\cdot {1.44}^8=75\cdot 18.488425889503635=1386.6319417127727$$

$$a_{10}=a_1·r^{n-1}=75\cdot {1.44}^{10-1}=75\cdot {1.44}^9=75\cdot 26.623333280885234=1996.7499960663924$$