Answer
The common difference is $3a+2b$
The next term of the sequence: $7a + 5b + c+(3a+2b)=10a+7b+c$
Work Step by Step
We are given: $a + b + c, 4a + 3b + c, 7a + 5b + c, ... $
To find the pattern of this sequence we have to find the difference between consecutive terms of the sequence.
2nd term and 1st term: $4a + 3b + c -(a + b + c)=3a+2b$
3rd term and 2nd term: $7a + 5b + c-(4a + 3b + c )=3a+2b$
The common difference is $3a+2b$. We use this pattern to get the next term of the sequence: $7a + 5b + c+(3a+2b)=10a+7b+c$
