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2 years ago

Please help me out!! :D

Mathematics

1 answer:

Rudik [331]2 years ago

7 0

$T_n = a_1 + d(n - 1)
$

$T_n = 52 + 12(n - 1)$

$T_n = 52 + 12n - 12$

$T_n = 40 + 12n$

When n = 102,
$T_{102} = 40 + 12(102) = 1264$

Answer: 1264

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The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?

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Step-by-step explanation:

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Given, 7th term is 10, we can write:

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We can solve for a in the first equation as:

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Now we can plug this into a of the 2nd equation:

$ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}$

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$a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640$

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:

$ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80$

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