Find the sum of number of stereoismomers and stereocentres for the given compound.
`CH_3-CH=CH-undersetunderset(Cl)(|)CH-CH=CH-CH_3`

Explanation

To find the sum of the number of stereoisomers and stereocenters for the given compound `CH₃-CH=CH(Cl)-CH-CH=CH-CH₃`, we will follow these steps:

### Step 1: Identify Stereocenters
1. **Identify the Stereocenters**:
- A stereocenter is typically a carbon atom that is bonded to four different groups.
- In the given compound, we can see that there are two double bonds (C=C) and one carbon atom with a chlorine substituent.
- The carbon atom with the chlorine (C) can be considered a stereocenter because it is bonded to different groups (Cl, H, and two different alkyl groups).
- The two double bonds can also give rise to stereoisomerism (cis-trans isomerism).

2. **Count the Stereocenters**:
- The compound has 3 stereocenters:
- One from the carbon with Cl (chiral center).
- Two from the double bonds (considered as pseudo stereocenters due to cis-trans isomerism).

### Step 2: Calculate the Number of Stereoisomers
3. **Use the Formula for Stereoisomers**:
- The formula for calculating the number of stereoisomers is \( 2^n \), where \( n \) is the number of stereocenters.
- Here, we have determined that there are 3 stereocenters.

4. **Calculate the Stereoisomers**:
- Using the formula:
\[ \text{Number of stereoisomers} = 2^3 = 8 \]

### Step 3: Sum the Stereocenters and Stereoisomers
5. **Sum the Values**:
- Now we add the number of stereocenters and the number of stereoisomers:
\[ \text{Sum} = \text{Number of stereocenters} + \text{Number of stereoisomers} = 3 + 8 = 11 \]

### Final Answer
The sum of the number of stereoisomers and stereocenters for the given compound is **11**.

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