MATH SOLVE

2 months ago

Q:
# Find A4 in the geometric series in which S4=65 and the common ratio is r=2/3Will give BRAILIEST for the RIGHT answer

Accepted Solution

A:

Answer:a₄ = 8Step-by-step explanation:The sum to n terms of a geometric sequence is[tex]S_{n}[/tex] = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]where a is the first term and r the common ratio, thus[tex]S_{4}[/tex] = [tex]\frac{a(1-2/3)^{4} }{1-\frac{2}{3} }[/tex] = 65, that is[tex]\frac{a(1-\frac{16}{81}) }{\frac{1}{3} }[/tex] = 653a × [tex]\frac{65}{81}[/tex] = 65[tex]\frac{195a}{81}[/tex] = 65 ( multiply both sides by 81 )195a = 5265 ( divide both sides by 195 )a = 27Hencea₂ = 27 × [tex]\frac{2}{3}[/tex] = 18a₃ = 18 × [tex]\frac{2}{3}[/tex] = 12a₄ = 12 × [tex]\frac{2}{3}[/tex] = 8