Converges and diverges part 2:

c. converges, 6

Step-by-step explanation:

An infinite geometric series converges if the absolute value of the common ratio is less than 1.

Here, the common ratio is 1/2:

| 1/2 | = 1/2 < 1

So the series converges.  The sum of an infinite geometric series is:

S = a₁ / (1 − r)

where a₁ is the first term and r is the common ratio.

Here, a₁ = 3 and r = 1/2:

S = 3 / (1 − 1/2)

S = 6

a² + b²= c²

24² + 7² = c²

c= 25