সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=75$$ এবং সাধারণ অনুপাত: $$r=0.32$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {0.32}^{2-1}=75\cdot {0.32}^1=75\cdot 0.32=24$$

$$a_3=a_1·r^{n-1}=75\cdot {0.32}^{3-1}=75\cdot {0.32}^2=75\cdot 0.1024=7.680000000000001$$

$$a_4=a_1·r^{n-1}=75\cdot {0.32}^{4-1}=75\cdot {0.32}^3=75\cdot 0.032768000000000005=2.4576000000000002$$

$$a_5=a_1·r^{n-1}=75\cdot {0.32}^{5-1}=75\cdot {0.32}^4=75\cdot 0.01048576=0.786432$$

$$a_6=a_1·r^{n-1}=75\cdot {0.32}^{6-1}=75\cdot {0.32}^5=75\cdot 0.0033554432000000006=0.25165824000000003$$

$$a_7=a_1·r^{n-1}=75\cdot {0.32}^{7-1}=75\cdot {0.32}^6=75\cdot 0.0010737418240000002=0.08053063680000001$$

$$a_8=a_1·r^{n-1}=75\cdot {0.32}^{8-1}=75\cdot {0.32}^7=75\cdot 0.00034359738368000005=0.025769803776000005$$

$$a_9=a_1·r^{n-1}=75\cdot {0.32}^{9-1}=75\cdot {0.32}^8=75\cdot 0.00010995116277760002=0.008246337208320001$$

$$a_{10}=a_1·r^{n-1}=75\cdot {0.32}^{10-1}=75\cdot {0.32}^9=75\cdot 3.518437208883201E-05=0.002638827906662401$$