A sequence of terms $a_1, a_2, a_3, \ldots$ is defined by: a_1 = 3 a_{n+1} = 8 - a_n (a) (i) Show that this sequence is periodic - Edexcel - A-Level Maths Pure - Question 5 - 2022 - Paper 2

The order of this periodic sequence is 2, as it repeats every 2 terms.

The value of the sum can be calculated by recognizing that the sequence alternates between 3 and 5.

For 85 terms, we find the number of odd and even indexed terms:

• Odd indexed: 43 terms are equal to 3 (since the first term is 3).
• Even indexed: 42 terms are equal to 5.

Thus, we can calculate the sum as follows:

$\sum_{n=1}^{85} a_n = 43 \cdot 3 + 42 \cdot 5 = 129 + 210 = 339.$