The first term of geometric sequence is 1/2 and the 9th term is 128. Find the sum of its 15 terms.
Answers
Given : The first term of geometric sequence is 1/2 and the 9th term is 128.
To Find : the sum of its 15 terms.
Solution:
geometric sequence
nth term = arⁿ⁻¹
a = first term = 1/2
r = common ratio
9th term is 128.
=> (1/2)r⁹⁻¹ = 128
=> r⁸ = 256
=> r⁸ = (±2⁸)
=> r = ±2
Sum of n term = a(rⁿ - 1)/(r - 1)
r = 2
sum of its 15 terms.
= (1/2)( 2¹⁵ - 1) /(2 - 1)
= ( 2¹⁵ - 1) /2
= 32,767/2
r = -2
sum of its 15 terms.
= (1/2)( (-2)¹⁵ - 1) /(-2 - 1)
= ( -2¹⁵ - 1) /(-6)
= 32,769/6
= 10,923/2
the sum of its 15 terms. = 32,767/2 or 10,923/2
16383.5 or 5461.5
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