Question 7 Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 …
Class X1 - Maths -Sequences and Series Page 192
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0.15 , 0.015 , 0.0015 ...........
if we modify this series , we get
15/(10)², 15/(10)³, 15/(10)⁴, .........
now,
first term (a) = 15/(10)²
common ratio (r) = 15/(10)³/15/(10)² = 1/10
use the formula,
S_n = a(1-rⁿ)/(1-r) , for, r < 1
S_20= 15/(10)² ( 1 - 1/10^20)/(1 - 1/10)
= 0.15{1 - (0.1)^20}/(1-0.1)
= 0.15{ 1 - (0.1)^20}/0.9
= 0.15 /0.9{1 - (0.1)^20}
hence, answer is { 1 - (0.1)^20}/6
if we modify this series , we get
15/(10)², 15/(10)³, 15/(10)⁴, .........
now,
first term (a) = 15/(10)²
common ratio (r) = 15/(10)³/15/(10)² = 1/10
use the formula,
S_n = a(1-rⁿ)/(1-r) , for, r < 1
S_20= 15/(10)² ( 1 - 1/10^20)/(1 - 1/10)
= 0.15{1 - (0.1)^20}/(1-0.1)
= 0.15{ 1 - (0.1)^20}/0.9
= 0.15 /0.9{1 - (0.1)^20}
hence, answer is { 1 - (0.1)^20}/6
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