To determine the correct sequence, let us identify the role of each reagent.

1. Identify the reagents

1. Tollen's reagent: $[Ag(NH_3)_2]^+OH^-$ This oxidizes an aldehyde to the corresponding carboxylate/carboxylic acid.

2. Grignard reagent: $CH_3MgBr$ This adds a methyl group to a carbonyl compound. It reacts with aldehydes/ketones, but it is destroyed by acidic proton sources.

3. Acidic methanol: $H^+/CH_3OH$ This is used for esterification of a carboxylic acid to the methyl ester.

2. Logical order of transformation

For such a sequence, the only sensible order is:

1. Oxidize aldehyde to carboxylic acid using Tollen's reagent.
2. Convert carboxylic acid to methyl ester using $H^+/CH_3OH$.
3. React ester with Grignard reagent $CH_3MgBr$, which ultimately gives a tertiary alcohol after hydrolysis.

Thus the sequence is: $[Ag(NH_3)_2]^+OH^- \rightarrow H^+/CH_3OH \rightarrow CH_3MgBr$

3. Check the options

Option A

$CH_3MgBr,\ H^+/CH_3OH,\ [Ag(NH_3)_2]^+OH^-$ Incorrect. Grignard reagent cannot be used first if oxidation and esterification are needed later in this manner.

Option B

$[Ag(NH_3)_2]^+OH^-,\ CH_3MgBr,\ H^+/CH_3OH$ Incorrect. After oxidation to acid, Grignard reagent will be quenched by the acidic proton of the carboxylic acid.

Option C

$[Ag(NH_3)_2]^+OH^-,\ H^+/CH_3OH,\ CH_3MgBr$ Correct. This is the proper order:

• aldehyde $\to$ acid
• acid $\to$ methyl ester
• ester $\to$ tertiary alcohol via Grignard reaction

Option D

$CH_3MgBr,\ [Ag(NH_3)_2]^+OH^-,\ H^+/CH_3OH$ Incorrect. Tollen's reagent is not used after Grignard addition in such a sequence.

4. Final answer

The correct sequence of reagents is: $\boxed{[Ag(NH_3)_2]^+OH^-,\ H^+/CH_3OH,\ CH_3MgBr}$

So, the correct option is C.