`a_1 = 0.375, a_(n + 1) = a_n + 0.26` Find the sum of the first 100 positive odd integers.

The positive integers are 1,3,5,7,9,..........

So the first term `a_1` is 1 and common difference d is 2 and number of terms n is 100.

`S_n=n/2(a_1+a_n)`

where `S_n`  is the sum of the n terms of the arithmetic sequence and `a_n` is the nth term.

`S_n=n/2(a_1+a_1+(n-1)d)`

`S_n=n/2(2a_1+(n-1)d)`

Now plug in the values of `a_1` ,d and n

`S_100=100/2(2*1+(100-1)2)`

`S_100=50(2+99*2)`

`S_100=50*100*2`

`S_100=10000`

So, the sum of the first 100 positive odd integers is 10000