Find the sum of the following without actually adding: 1+3+5+7+9+11+13+15

use this formula Sn=n/2[2a+(n-1)d]

here,d=a2-a1 and n= no. Of terms

Step-by-step explanation:

S8=8/2[2(1)+(8-1)2]

S8=64

Step-by-step explanation:

The following numbers are successive odd numbers.

The sum of successive odd numbers (starting from 1) is always the square of number of terms you are adding.

Hear there are 8 terms. Square of 8 is 64.

Hence the sum of this numbers is 64.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

step-by-step explanation:

. your answer will contain x - and y -terms. (1 point) x ( ¿¿ 2 − 7 ) 2 +( y 2 − 9 ) 2 √ ¿ 12. what is the distance from the directrix (the crocodile river) to the point ( x , y )? write this equation. your answer will contain a y -term.