সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=144$$ এবং সাধারণ অনুপাত: $$r=0.013888888888888888$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=144$$

$$a_2=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{2-1}=144\cdot {0.013888888888888888}^1=144\cdot 0.013888888888888888=2$$

$$a_3=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{3-1}=144\cdot {0.013888888888888888}^2=144\cdot 0.00019290123456790122=0.027777777777777776$$

$$a_4=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{4-1}=144\cdot {0.013888888888888888}^3=144\cdot 2.679183813443072E-06=0.0003858024691358024$$

$$a_5=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{5-1}=144\cdot {0.013888888888888888}^4=144\cdot 3.721088629782045E-08=5.358367626886144E-06$$

$$a_6=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{6-1}=144\cdot {0.013888888888888888}^5=144\cdot 5.168178652475062E-10=7.442177259564088E-08$$

$$a_7=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{7-1}=144\cdot {0.013888888888888888}^6=144\cdot 7.178025906215363E-12=1.0336357304950123E-09$$

$$a_8=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{8-1}=144\cdot {0.013888888888888888}^7=144\cdot 9.969480425299115E-14=1.4356051812430725E-11$$

$$a_9=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{9-1}=144\cdot {0.013888888888888888}^8=144\cdot 1.3846500590693213E-15=1.9938960850598227E-13$$

$$a_{10}=a_1·r^{n-1}=144\cdot {0.013888888888888888}^{10-1}=144\cdot {0.013888888888888888}^9=144\cdot 1.923125082040724E-17=2.7693001181386427E-15$$