How many times, on average, do you need to toss a single unbiased coin to get 5 times 'heads' in a row?

Question

If you toss a coin ten times and it lands heads up every time, what is the probability that it will land heads up if you toss it again?

Answer 1

Probability of landing 5 heads in a row = 1/32
Let the number of coin flips required to land 5 heads in a row be 'a'
a = 5×(1/32){5 heads in a row} + (a+1)(1/2){first flip was tails} + (a + 2)(1/4){2 flips wasted on tails} + (a + 3)(1/8){3 flips wasted on tails} + (a + 4)(1/16){4 flips wasted on tails} + (a + 5)(1/32){5 flips wasted on tails}
on simplifying
a = 62. So we need 62 tosses on average to get 5 heads in a row.