# Find five numbers in G. P. such that their product is 1024 and fifth term is square of the third term. - Mathematics and Statistics

Sum

Find five numbers in G. P. such that their product is 1024 and fifth term is square of the third term.

#### Solution

Let the five numbers in G. P. be

"a"/"r"^2, "a"/"r", "a", "ar", "ar"^2

According to the given conditions,

"a"/"r"^2 xx "a"/"r" xx "a" xx "ar" xx "ar"^2 = 1024

∴ a5 = 45
∴ a = 4                   ...(i)
Also, ar2 = a2
∴ r2 = a
∴ r2 = 4            ...[From (i)]
∴ r = ±2
When a = 4, r = 2

"a"/"r"^2 = 1, "a"/"r" = 2, a = 4, ar = 8, ar2 = 16

When a = 4, r = – 2

"a"/"r"^2 = 1, "a"/"r" =  – 2, a = 4, ar = – 8, ar2 = 16

∴  the five numbers in G.P. are
1, 2, 4, 8, 16 or – 2, 4, – 8, 16.

Concept: Sequence and Series - Geometric Progression (G.P.)
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 4 Sequences and Series
Exercise 4.1 | Q 8 | Page 51