the first term of a geometeic series is 1, the common ratio is 2, and the sum of the series is 63. How many terms are there in this geonetric series?​

Answer:6 termsStep-by-step explanation:To find the number of terms we will use the formula:Sn = a(1-r^n)/1-rwhere a is the first term= 1r is the common ratio = 2Sn is the sum of series = 63n is the number of terms = ?Now substitute the values in the formula:Sn = a(1-r^n)/1-r63= 1(1-2^n)/1-263=1(1-2^n)/-163*-1 = 1(1-2^n)-63 = 1-2^nNow combine the constants:-63-1= -2^n-64= -2^n64= 2^n2^6 = 2^nWhen the base are same powers are equal to each other.6=nThus there are 6 terms....