Math, asked by dksaaho1234567, 11 months ago

Which term of Gp 1/4,4,16...is equal to 16th term of Gp 2,4,8....​

Answers

Answered by eudora
1

10th term of first G.p. will be equal to 16th term of second G.P.

Step-by-step explanation:

For any geometric progression nth term is defined by the expression :

T_{n}=ar^{n-1}

where : a = first term of the sequence

             r = common ratio of the sequence

             n = number of term

For G.P. \frac{1}{4},1,4,16....

T_{n}=ar^{n-1}

    = \frac{1}{4}(4)^{n-1}

    = 4^{n-2}

For G.P. 2, 4, 8........

T_{n}=ar^{n-1}

T_{16}=2(2)^{16-1}

Since T_{n} of first G.P. = T_{16} of second G.P.

4^{n-2} = 2(2)^{16-1}

2^{2(n-2)}=2^{16}

2(n-2) = 16

2n - 4 = 16

2n = 20

n = 10

Therefore, 10th term of first G.p. will be equal to 16th term of second G.P.

Learn more about geometric progression : https://brainly.in/question/11281733

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