Answer: the first term of the series is 128
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
From the information given,
r = 1/4 = 0.25
n = 4
S4 = 170
Therefore, the expression for the sum of the 4 terms, S4 is
170 = a(1 - 0.25^4)/(1 - 0.25)
170 = a(1 - 0.00390625)/(1 - 0.25)
170 = a(0.99609375)/(0.75)
170 = 1.328125a
a = 170/1.328125
a = 128
Y = 2 ( X - 3 ) ^ 2 - 4 =-4
Answer:
Area of the rectangular Field = 3 8/9 km²
Step-by-step explanation:
Length of the field = 2 1/3 km
Width of the field = 1 2/3 km
Area of a rectangular Field = length × width
= 2 1/3 × 1 2/3
= 7/3 × 5/3
= (7*5)/(3*3)
= 35/9
Area of the rectangular Field = 3 8/9 km²
Perimeter of the rectangular Field = 2(length + width)
= 2(2 1/3 + 1 2/3)
= 2(7/3 + 5/3)
= 2(7+5/3)
= 2(12/3)
=2(4)
= 8 km
Perimeter of the rectangular Field = 8 km