Question 738254
<pre>
1,2,0.5,5,0.25,8..... 

Change the decimals to fractions:

1,  2, {{{1/2}}}, 5, {{{1/4}}}, 8, ...

the odd numbered terms are 50 terms of this geometric sequence

1, {{{1/2}}}, {{{1/4}}}, ...

We use the formula 

S<sub>n</sub> = {{{a[1](1-r^n)/(1-r)}}} 

where n=50, a<sub>1</sub> = 1, r = {{{1/2}}}

S<sub>50</sub> = {{{1(1-(1/2)^50)/(1-1/2)}}} 

Since {{{(1/2)^50}}} is so small it is negligible and

that is essentially {{{1/(1/2)}}} = 2

the even numbered terms are 50 terms of this arithmetic sequence

2,5,8,...

We use the formula

S<sub>n</sub> = {{{n/2}}}[2a<sub>1</sub> + (n-1)d]

S<sub>50</sub> = {{{50/2}}}[2·2 + (50-1)3]

S<sub>50</sub> = 25[4 + 49·3]

S<sub>50</sub> = 3775

Answer:  2 + 3775 = 3777. 

Edwin</pre>