If the sum of three number in G.P is 13 12 and their product is - 1 , then find the numbers.

Given, the sum of three numbers in G.P 13 12 and their product is - 1 So let the three terms in G.P be a r , a & ar . Then according to the question, a r × a × ar = - 1 ⇒ a 3 = - 1 3 ⇒ a = - 1 Also, their sum will be, a r + a + ar = 13 12 ⇒ - 1 r - 1 - r = 13 12 ⇒ - 1 - r - r 2 r = 13 12 ⇒ - 12 - 12 r - 12 r 2 = 13 r ⇒ 12 r 2 + 25 r + 12 = 0 Solving, 12 r 2 + 25 r + 12 = 0 ⇒ 12 r 2 + 16 r + 9 r + 12 = 0 ⇒ 3 r + 4 4 r + 3 = 0 ⇒ r = - 4 3 or r = - 3 4 Hence, the series will be either - 4 3 , - 1 , - 3 4 or - 3 4 , - 1 , - 4 3 .

E M B I B E

All In One ICSE Mathematics Class 10>Chapter 9 - Arithmetic and Geometric Progression>Topic Exercise>Q 12

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10th ICSE

IMPORTANT

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If the $4^{t h}$ , $10^{t h}$ and $16^{t h}$ terms of a GP are $x, y, z$ respectively. Prove that $x, y, z$ are in GP.

Important Questions on Arithmetic and Geometric Progression

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IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 9 - Arithmetic and Geometric Progression>Topic Exercise>Q 13

If the

p^{t h}, q^{t h}

and

r^{t h}

terms of a GP are

a, b

and

c

respectively. Prove that

a^{q - r} b^{r - p} c^{p - q} = 1

.

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 9 - Arithmetic and Geometric Progression>Topic Exercise>Q 14

If the first and

n^{t h}

terms of a GP are

a

and

b

respectively and

P

is the product of

n

terms, then prove that

P^{2} = {(a b)}^{n}

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IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 9 - Arithmetic and Geometric Progression>Topic Exercise>Q 15

Find the term of the following G.P,

6^{th}

term from the end of the G.P,

8, 4, 2 . . . . . . . . . \frac{1}{1024}

?

MEDIUM

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IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 9 - Arithmetic and Geometric Progression>Topic Exercise>Q 15

Find the $4 th$ term from end of the G.P: $8, 4, 2, . . ., \frac{1}{1024}$

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IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 9 - Arithmetic and Geometric Progression>Topic Exercise>Q 16

Prove that in a finite GP the product of the terms equidistant from the beginning and the end is always same and equal to the product of first and last term.

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 9 - Arithmetic and Geometric Progression>Topic Exercise>Q 17

If the sum of three number in G.P is