1. 1. Find these terms of the sequence {an}, where an = 2 (−3)n + 5n.a) a0 b) a1 c) a4 d) a5

1. Break Down the Problem

We need to find specific terms of the sequence defined by the formula $a_n = 2(-3)^n + 5n$. The terms we want to find are $a_0$, $a_1$, $a_4$, and $a_5$.

2. Relevant Concepts

The sequence is given by the formula $a_n = 2(-3)^n + 5n$. To find the terms, we will substitute the values of $n$ into this formula.

3. Analysis and Detail

We will calculate each term one by one:

1. Calculate $a_0$: $a_0 = 2(-3)^0 + 5(0) = 2(1) + 0 = 2$

2. Calculate $a_1$: $a_1 = 2(-3)^1 + 5(1) = 2(-3) + 5 = -6 + 5 = -1$

3. Calculate $a_4$: $a_4 = 2(-3)^4 + 5(4) = 2(81) + 20 = 162 + 20 = 182$

4. Calculate $a_5$: $a_5 = 2(-3)^5 + 5(5) = 2(-243) + 25 = -486 + 25 = -461$

4. Verify and Summarize

We have calculated each required term:

• $a_0 = 2$
• $a_1 = -1$
• $a_4 = 182$
• $a_5 = -461$

Final Answer

• $a_0 = 2$
• $a_1 = -1$
• $a_4 = 182$
• $a_5 = -461$