Use sigma notation to represent the following series for the first 10 terms.

3 + (-6) + 12 + (-24) + ⋯

The sum of 10 terms is  S₁₀  =  -1023

Step-by-step explanation:

Explanation:-

Given series

3 + (-6) + 12 + (-24) + ⋯

This is geometric sequence  3 , -6 ,12 , -24 ,....

a = 3 and common ratio    

Given ratio r = -2 < 1

Sum of 'n' terms of a G.P

Sum of '10' terms of a G.P

Conclusion:-

Sum of '10' terms of a G.P = - 1023

Verification:-

The series of first 10 terms

3+(-6)+12+(-24)+48+(-96)+192+(-384)+768+(-1536) =  -1023

step-by-step explanation:

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).