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Find the nth term in the geometric sequence 12, -3, 3/4

1 Answer

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Answer:

12 (-0.25)ⁿ

Explanation:

recall that the general form for each term in the geometric progression is

arⁿ

such that the geometric progression looks something like.

ar⁰, ar¹, ar², ar³, ....., arⁿ, ......

also note that r⁰ = 1, hence ar⁰ is simply a

hence the G.P can be written

a, ar, ar², ar³, ....., arⁿ, ......

also note that r can be obtained by simply dividing the 2nd term with the 1stterm. i.e

r = ar ÷ a

now we are given the first 3 terms in the GP as

12, -3, 3/4, ....

comparing with the GP in the previous paragraph, we can see that ,

a = first term = 12

also

r = 2nd term ÷ 1st term

= -3 ÷ 12

= -0.25

hence the nth term

= arⁿ

= 12 (-0.25)ⁿ

User Islam Yahiatene
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