Study the following alphabetical sequence carefully:
$$\text{GAGHUTAAKHGAOYYDKKVRABICDDCRFFAHAHAIH}$$

The sum of the number of consonants and the number of vowels in the above series is:

The sum of the number of consonants and the number of vowels is simply equal to the total number of letters present in the given string sequence.
Let's count the total number of characters in the sequence:

$$\text{G(1) A(2) G(3) H(4) U(5) T(6) A(7) A(8) K(9) H(10)}$$

$$\text{G(11) A(12) O(13) Y(14) Y(15) D(16) K(17) K(18) V(19) R(20)}$$

$$\text{A(21) B(22) I(23) C(24) D(25) C(26) D(27) R(28) F(29) F(30)}$$

$$\text{A(31) H(32) A(33) H(34) A(35) I(36) H(37)}$$

Counting carefully from left to right, there are exactly $37$ characters in total.
Thus, $\text{Consonants}+\text{Vowels}=37$.