Mathematics, 10.10.2021 15:20 hermine40
Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms
Answers: 1
. Next term is obtained by multiplying half to the previous term . Notice the terms beginning from 2nd term , 
. Next term is obtained by adding 3 to the previous term . 
.![\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]](/tpl/images/2499/8133/59495.png)
will be too small , so we can neglect it and take its approximation as 0 .![\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]](/tpl/images/2499/8133/37fd0.png)
![\implies S_2=\dfrac{n}{2}[2a + (n-1)d]](/tpl/images/2499/8133/337cd.png)
![\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}](/tpl/images/2499/8133/4fd8b.png)
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Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms...
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