Question

Find the 5th term of the GP is 48 and it 8th term is 384. find the first term and the common​

Answer 1

`\text{1st term} = 3\\\\\text{Common ratio} = 2`

Step by step explanation:

`\text{Given that,}\\\\\text{5th term} = ar^(5-1) = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^(8-1) = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) / (i):\\\\~~~~~~(ar^7)/(ar^4)=(384)/(48)\\\\\implies r^(7-4) = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = (48)/(16)\\\\\implies a = 3\\`