Question

find the 10th twrm and the general rerm of the progression 1/4,-1/2,1,-2​

Answer 1

Answer:

In the given progression, we have

(−12)÷14=(−12×4)=−2,1÷(−12)=1×(−2)=−2,

(−2)÷1=−2 and 4÷(−2)=−2.

So, the given progression is a GP in which a=14 and r=−2.

∴ the 10th term, T 10 = ar (10−1)=ar 9=14×(−2)9=−5124=−128.

The general term, Tn= ar (n−1)= 14×(−2)(n−1)=  (−1)(n−1)×2(n−3)

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Answer 2

Step-by-step explanation:

Here, the given series is geometric progression.

And sign changes at each terms, ratio will be negative and next term can be obtained by multiplying the previous term to 2.

So, a = 1/4 and r = -2,

general term of GP can be written as,

T = a * r^(n-1),

so, it is T = (1/4) * (-2)^ (n-1)

10th term is,

(1/4) * (-2)^9 (negative sign)

= - (1/4) (2)^9

= -128

Answer : -128

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