What is the 87th term of the arithmetic sequence?

−1352,−1334,−1316,−1298,−1280,...

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What is the limit of the infinite series?Enter your answer in the box. Enter any fraction as a simplified fraction. ∑n=1∞(3n54n5+1)/ it's in the picture you'll read it.

How is the sum expressed in sigma notation?/also in picture.

1/64+1/16+1/4+1+4

The first term of a geometric sequence is −2100 . The common ratio of the sequence is −0.1 .

What is the 7th term of the sequence?

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The first term of a geometric sequence is 48, and the 5th term of the sequence is 24316 .

What are the geometric means between these terms?

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MathPhys MathPhys · Answer 1 · 2020-01-16T20:17:27+01:00

Step-by-step explanation:

1) The first term is -1352, and the common difference is 18. So the 87th term is:

a = -1352 + 18 (87 − 1)

a = 196

2) 1/64 + 1/16 + 1/4 + 1 + 4

This is a geometric series, where the first term is 1/64 and the common ratio is 4.

∑⁵ᵢ₌₁ 1/64 (4)ⁱ⁻¹

Since 1/64 = 4⁻³:

∑⁵ᵢ₌₁ 4⁻³ (4)ⁱ⁻¹

∑⁵ᵢ₌₁ (4)ⁱ⁻⁴

3) The first term is -2100, and the common ratio is -0.1, so the 7th term is:

a = -2100 (-0.1)⁷⁻¹

a = -0.0021

4) The first term is 48, and the fifth term is 243/16, so the common ratio is:

243/16 = 48 r⁵⁻¹

81/256 = r⁴

r = 3/4

So the sequence is:

48, 36, 27, 81/4, 243/16