সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=140$$ এবং সাধারণ অনুপাত: $$r=1.5$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=140$$

$$a_2=a_1·r^{n-1}=140\cdot {1.5}^{2-1}=140\cdot {1.5}^1=140\cdot 1.5=210$$

$$a_3=a_1·r^{n-1}=140\cdot {1.5}^{3-1}=140\cdot {1.5}^2=140\cdot 2.25=315$$

$$a_4=a_1·r^{n-1}=140\cdot {1.5}^{4-1}=140\cdot {1.5}^3=140\cdot 3.375=472.5$$

$$a_5=a_1·r^{n-1}=140\cdot {1.5}^{5-1}=140\cdot {1.5}^4=140\cdot 5.0625=708.75$$

$$a_6=a_1·r^{n-1}=140\cdot {1.5}^{6-1}=140\cdot {1.5}^5=140\cdot 7.59375=1063.125$$

$$a_7=a_1·r^{n-1}=140\cdot {1.5}^{7-1}=140\cdot {1.5}^6=140\cdot 11.390625=1594.6875$$

$$a_8=a_1·r^{n-1}=140\cdot {1.5}^{8-1}=140\cdot {1.5}^7=140\cdot 17.0859375=2392.03125$$

$$a_9=a_1·r^{n-1}=140\cdot {1.5}^{9-1}=140\cdot {1.5}^8=140\cdot 25.62890625=3588.046875$$

$$a_{10}=a_1·r^{n-1}=140\cdot {1.5}^{10-1}=140\cdot {1.5}^9=140\cdot 38.443359375=5382.0703125$$