# Geometric progression with some given terms

**Situation**

The 4^{th} term of a geometric progression is 6 and the 10^{th} term is 384.

Part 1: What is the common ratio of the G.P.?

A. 1.5

B. 3

C. 2.5

D. 2

Part 2: What is the first term?

A. 0.75

B. 1.5

C. 3

D. 0.5

Part 3: What is the seventh term?

A. 24

B. 32

C. 48

D. 96

**Solution**

Given

$a_4 = 6$

$a_4 = 6$

$a_{10} = 384$

Formula

$a_n = a_m r^{n - m}$

$a_{10} = a_4 r^{10 - 4}$

$384 = 6r^6$

$r^6 = 64$

$r = 2$ → Common ratio Answer for Part 1: [ D ]

$a_4 = a_1 r^{4 - 1}$

$6 = a_1 2^3$

$a_1 = 0.75$ → First term Answer for Part 2: [ A ]

$a_7 = a_4 r^{7 – 4}$

$a_7 = 6(2^3)$

$a_7 = 48$ → Seventh term Answer for Part 3: [ C ]

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