Question 307207
these are two different types of series, so the solution techniques are different


plan 1 is a GEOMETRIC series, any term equals the previous term MULTIPLIED by some constant (in this case, 2)


plan 2 is an ARITHMETIC series, any term equals the previous term with some constant ADDED (in this case, 5)


the sum of the arithmetic series is straightforward, if you think about it


the first term is some number,"a"
___ to find any term, "n", the equation is ___ a + (n-1)d
___ where "n" is the number of the term and "d" is the difference (added constant)


now look at plan 2 ___ a = 20 ___ d = 5
___ 1st term is 20 and 64th term is [20 + (63 * 5)] or 335 ___ the sum of these terms is 355
___ 2nd term is 25 and 63rd term is 330 ___ the sum of these terms is 355


see the pattern


for a series of N terms ___ take the sum of the pairs of terms (first and last)
___ divide by two to get an "average" term value
___ then multiply by the number of terms to get the sum of the series
___ s = ([a + (a + [(N-1)d])] / 2) * N = aN + ([(N^2-N)d] / 2)


for plan 2 ___ s = 20(64) + ([(4096 - 64)5] / 2) = 1280 + 10080 = 11360