সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=78$$ এবং সাধারণ অনুপাত: $$r=12.820512820512821$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=78$$

$$a_2=a_1·r^{n-1}=78\cdot {12.820512820512821}^{2-1}=78\cdot {12.820512820512821}^1=78\cdot 12.820512820512821=1000$$

$$a_3=a_1·r^{n-1}=78\cdot {12.820512820512821}^{3-1}=78\cdot {12.820512820512821}^2=78\cdot 164.36554898093362=12820.512820512822$$

$$a_4=a_1·r^{n-1}=78\cdot {12.820512820512821}^{4-1}=78\cdot {12.820512820512821}^3=78\cdot 2107.2506279606873=164365.5489809336$$

$$a_5=a_1·r^{n-1}=78\cdot {12.820512820512821}^{5-1}=78\cdot {12.820512820512821}^4=78\cdot 27016.03369180369=2107250.6279606875$$

$$a_6=a_1·r^{n-1}=78\cdot {12.820512820512821}^{6-1}=78\cdot {12.820512820512821}^5=78\cdot 346359.4063051755=27016033.69180369$$

$$a_7=a_1·r^{n-1}=78\cdot {12.820512820512821}^{7-1}=78\cdot {12.820512820512821}^6=78\cdot 4440505.209040712=346359406.3051755$$

$$a_8=a_1·r^{n-1}=78\cdot {12.820512820512821}^{8-1}=78\cdot {12.820512820512821}^7=78\cdot 56929553.96206041=4440505209.040711$$

$$a_9=a_1·r^{n-1}=78\cdot {12.820512820512821}^{9-1}=78\cdot {12.820512820512821}^8=78\cdot 729866076.436672=56929553962.06042$$

$$a_{10}=a_1·r^{n-1}=78\cdot {12.820512820512821}^{10-1}=78\cdot {12.820512820512821}^9=78\cdot 9357257390.213743=729866076436.672$$