Question

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

3 + (-6) + 12 + (-24) + ⋯

Answer 1

Answer:

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  $r = \frac{-6}{3} = -2$  

Given ratio r = -2 < 1

Sum of 'n' terms of a G.P

$S_{n} = \frac{a(1-r^{n} ) }{1-r} if r <1$

Sum of '10' terms of a G.P

$S_{10} = \frac{3((1-(-2 )^{10} }{1-(-2)}$

$S_{10} = \frac{3((1-(-2 )^{10} }{3} = 1-2^{10} = 1- 1024 = - 1023$

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