সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=78$$ এবং সাধারণ অনুপাত: $$r=0.5384615384615384$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=78$$

$$a_2=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{2-1}=78\cdot {0.5384615384615384}^1=78\cdot 0.5384615384615384=42$$

$$a_3=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{3-1}=78\cdot {0.5384615384615384}^2=78\cdot 0.28994082840236685=22.615384615384613$$

$$a_4=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{4-1}=78\cdot {0.5384615384615384}^3=78\cdot 0.15612198452435136=12.177514792899405$$

$$a_5=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{5-1}=78\cdot {0.5384615384615384}^4=78\cdot 0.08406568397465074=6.557123350022757$$

$$a_6=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{6-1}=78\cdot {0.5384615384615384}^5=78\cdot 0.04526613752481193=3.53075872693533$$

$$a_7=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{7-1}=78\cdot {0.5384615384615384}^6=78\cdot 0.024374074051821806=1.901177776042101$$

$$a_8=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{8-1}=78\cdot {0.5384615384615384}^7=78\cdot 0.013124501412519434=1.0237111101765157$$

$$a_9=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{9-1}=78\cdot {0.5384615384615384}^8=78\cdot 0.007067039222125849=0.5512290593258162$$

$$a_{10}=a_1·r^{n-1}=78\cdot {0.5384615384615384}^{10-1}=78\cdot {0.5384615384615384}^9=78\cdot 0.0038053288119139182=0.2968156473292856$$