Question

BRAINLIEST + POINTS!! SHOW WORK PLEASE!

Answer 1

nth term = -4 (1/3)^(n-1)

a). first four terms...

first term (n=1) : -4
2nd term (n=2) : -4/3
3rd term (n=3). : -4/9
4th term (n=4) : -4/27

b) the series converges ...
because as n tends to infinity, nth term tends to zero.. and Sum of the series gets some finite value...

c) sum of infinite geometric series = a / ( 1 - r )

after taking (-4) as common,

here, a = 1, r = 1/3
so, the sum =

$- 4 \times (1 + \frac{1}{3} + \frac{1}{3^{2} } + \frac{1}{ {3}^{3} } + ...) \\ = - 4 \times ( 1 \div (1 - \frac{1}{3} )) \\ = - 4 \times ( 1 \times \frac{3}{2} ) \\ = -6$