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tamaranim1 [39]
3 years ago
10

The sum of the first three terms of geometric sequence is 14. If the first term is 2, find the possible values of the sum of the

first 5 terms.
Mathematics
2 answers:
Scorpion4ik [409]3 years ago
7 0

We have a first term of 2 and a common ratio of <em>r</em>. We're told

2 + 2r + 2r^2 = 14

r^2 +r  - 6 = 0

(r+3)(r-2)=0

r=-3 \textrm{ or } r=2

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

Irina18 [472]3 years ago
4 0

Geometric series are in the form of

a +a*r +a*r^2+...

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

And it is given that

2 +2*r +2*r^2=14

2r^2+2r-12=0

r^2 +r-6=0

(r+3)(r-2)=0

r=-3,2

So the first five terms are

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

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

= 122 or 62

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