I assume that you are looking for the first term (a1) given the sum and ratio of the first five terms of a geometric sequence
Formula: Sn = a1 (1-r^n)
1-r
n = 5; S5= 31/4; r (ratio) = 1/2; a1=unknown
31/4 = a1 (1-(1/2)^5)
1-1/2
31/4 = a1 (1-1/32)
1/2
31/4 = a1 (31/32)
1/2
(1/2)(31/4) = a1 (31/32)
31/8 = a1 (31/32)
(32/31)(31/8) = a1 (31/32)(31/31)
4 = a1
FINAL ANSWER: a1 = 4 (the first term of the first five terms of a geometric sequence given their sum and ratio)
