A sequence of numbers $a_1, a_2, a_3, \ldots$ is defined by \[ a_{n+1} = 5a_n - 3, \quad n \geq 1 \] Given that $a_2 = 7$, (a) find the value of $a_1$ - Edexcel - A-Level Maths Pure - Question 7 - 2014 - Paper 1

We first need to find the subsequent terms $a_3$ and $a_4$.

1. For $n=2$:
   [ a_{3} = 5a_{2} - 3 = 5 \times 7 - 3 = 35 - 3 = 32 ]
2. For $n=3$:
   [ a_{4} = 5a_{3} - 3 = 5 \times 32 - 3 = 160 - 3 = 157 ]
   Now, we can sum the first four terms:
   [ \sum_{r=1}^4 a_r = a_1 + a_2 + a_3 + a_4 = 2 + 7 + 32 + 157 ]
   Calculating gives:
   [ \sum_{r=1}^4 a_r = 198 ]
   Therefore, the value is 198.