Sequences And Series

We treat the 1 % increase per year as exponential growth over 15 years (from 2020 to 2035):Initial temperature: Annual growth factor: Number of years: Future temperature:$ $That matches Option B.

To determine the progression of the sequence , we analyze the given condition for the sequence's sum: This expression resembles the sum formula for an arithmetic progression (AP): To validate if our sequence is an AP, let's assume it is. If so, the sum formula for the first terms of an AP, where is the first term and is the common difference, would be: Substituting these into the given equation: Simplifying both sides gives: This reduces further to: Since , this confirms our sequence is indeed an arithmetic progression (AP), given that this assumption led to a consistent and valid result. Therefore, the assumption that is an arithmetic progression is correct.

We are told: But .So Step 1:We can write equations for different .For etc.At : At : Now subtract the two: Simplify: Step 2:So we have the recurrence: This means the sequence increases by 13 every 3 steps (since ).So for :These indices differ by : ✅Final Answer: Answer: Option A (13)