Question

[BRAINLIEST]The fourth term of a geometric sequence is 27 and the seventh term is 1. What is the first term?

Answer 1

Answer:

729

Step-by-step explanation:

Let the first term be a and the common ratio r

Use the formula for the n'th term: xn = arn − 1

The fourth term = 27 ⇒ x4 = ar4 − 1 = 27 ⇒ ar3 = 27 (1)

The seventh term = 1 ⇒ x7 = ar7 − 1 = 1 ⇒ ar6 = 1 (2)

Divide (2) by (1) ⇒ r3 = 1/27 ⇒ r = 1/3

Substitute r = 1/3 into (1) ⇒ a × (1/3)3 = 27 ⇒ a × 1/27 = 27  

⇒ a = 27 × 27 = 729  

The first term is 729

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Answer 2

Hello user


Let the first term be a and commone ratio be r

So, according to the question,

ar^3 = 27 .....(1)

ar^6 = 1 ......(2)

(2) / (1) , we get

r^3 = 1/27

r = 1/3

Putting r = 1/3 in eq(1), we get

a × 1/27 = 27

a = 729

So , first term is 729.


hope it works