Q. 6 - Calculus

Question

Consider the sequence A(1), A(2), A(3),.....,A(n) write our the sequence up to n. What do you notice?

Step-by-Step Solution

Answer

The first 10 terms of the sequence are

$$\begin{gathered} A\left(1\right)=7 \\ A\left(2\right)=11.9 \\ A\left(3\right)=15.33 \\ A\left(4\right)=17.73 \\ A\left(5\right)=19.41 \\ A\left(6\right)=20.58 \\ A\left(7\right)=21.40 \\ A\left(8\right)=21.97 \\ A\left(9\right)=22.37 \\ A\left(10\right)=22.65 \end{gathered}$$

Step 1: Given information

Our given sequence is $\sum _{k=1}^{n}10{(0.7)}^k$

Step 2: Find First 10 terms of the sequence

We have,

$$\begin{gathered} A\left(1\right)=7 \\ A\left(2\right)=11.9 \\ A\left(3\right)=15.33 \\ A\left(4\right)=17.73 \\ A\left(5\right)=19.41 \\ A\left(6\right)=20.58 \\ A\left(7\right)=21.40 \\ A\left(8\right)=21.97 \\ A\left(9\right)=22.37 \\ A\left(10\right)=22.65 \end{gathered}$$