Respuesta :

Riia

Geometric series are in the form of

[tex] a +a*r +a*r^2+... [/tex]

Where a is the first term and r is the common ratio .

And it is given that

[tex] 2 +2*r +2*r^2=14 [/tex]

[tex] 2r^2+2r-12=0 [/tex]

[tex] r^2 +r-6=0 [/tex]

[tex] (r+3)(r-2)=0 [/tex]

r=-3,2

So the first five terms are

[tex] 2+2(-3)+2(-3)^2+2(-3)^3+2(-3)^4 or 2+2(2)+2(2)^2+2(2)^3+2(2)^4 [/tex]

= 2-6+18-54+162 or 2+4+8+16+32

= 122 or 62

DeanR

We have a first term of 2 and a common ratio of r. We're told

[tex]2 + 2r + 2r^2 = 14[/tex]

[tex]r^2 +r - 6 = 0[/tex]

[tex](r+3)(r-2)=0[/tex]

[tex]r=-3 \textrm{ or } r=2[/tex]

If r=-3 the fourth term is 2((-3)³) and the fifth 2((-3)^4) for a sum of

14 - 54 + 162 = 122

If r=2 the remaining terms are 2(2^3)=16 and 2(2^4)=32 for a sum of

14 + 16 + 32 = 62

Answer: 62 or 122

Otras preguntas