Find s5 for the series -2 + -10 + -50 + -250 + find s12 for the series 1 + 1.5 + 2.25 + 3.375 + find s12 for the series 1 + 2 + 4 + 8 +

Let us check series : -10 /-2 = 5 -50/-10 = 5

so it is a geometric series with a= -2 and r= 5

sum formula for n terms of geometric series = a ( r^n -1 ) /( r-1)

here we find S5 that is n= 5 = -2 ( 5^ 5 - 1) /( 5-1)

= -2 ( 3125 -1) / 4 = -1562

second series is : 1.5/1 = 1.5 2.25/1.5 = 1.5

this is also geometric series but n = 12 a= 1 and r= 1.5

we use same formula

S12 = 1 ( (1.5) ^12 -1) /( 1.5-1) =

128.74 / 0.5 = 257.49

Last is 2/1= 2 4/2 = 2 8/4 = 2 so r = 2 a = 1 and n = 12

we use same formula 1 ( 2^12 - 1) / (2-1)

= 4095

Answers : -1562 , 257.49 , 4095

-10 /-2 = 5 -50/-10 = 5, it is a geometric series with a= -2 and, r= 5. sum formula for n terms of geometric series is = a ( r^n -1 ) /( r-1)

here S5 that is n= 5 = -2 ( 5^ 5 - 1) /( 5-1) = -2 ( 3125 -1) / 4 = -1562

2nd series is : 1.5/1 = 1.5 2.25/1.5 = 1.5

this is also geometric series but n = 12 a= 1 and r= 1.5

we use same formula

S12 = 1 ( (1.5) ^12 -1) /( 1.5-1) =

128.74 / 0.5 = 257.49

Last is 2/1= 2 4/2 = 2 8/4 = 2 so r = 2 a = 1 and n = 12

we use same formula 1 ( 2^12 - 1) / (2-1)

= 4095

Answers : -1562 , 257.49 , 4095

the first one, all those points on the line just make a strait line.