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Chapter 19: Problem 1

Find the 23 rd term of an arithmetic sequence with first term 2 and common difference \(7 .\)

Short Answer

Expert verified
Answer: The 23rd term of the arithmetic sequence is 156.

Step by step solution

01

Understand the arithmetic sequence formula

The arithmetic sequence formula is used to find the nth term of an arithmetic sequence. It is given by: \(T_n = a + (n-1)d\) For our given problem: \(a = 2\): first term \(n = 23\): term position \(d = 7\): common difference
02

Plug values into the formula

Now that we have all the required values, we can plug them into the arithmetic sequence formula: \(T_n = a + (n-1)d\) And place all known values: \(T_{23} = 2 + (23-1)7\)
03

Simplify the expression

Now we'll simplify the expression: \(T_{23} = 2 + (22)7\) \(T_{23} = 2 + 154\) \(T_{23} = 156\)
04

State the final answer

The 23rd term of the arithmetic sequence with first term 2 and common difference 7 is: \(T_{23} = 156\)

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Most popular questions from this chapter

Use the power series expansion of \(\cos x\) to show that $$ \cos \frac{x}{2}=1-\frac{x^{2}}{8}+\frac{x^{4}}{384}-\frac{x^{6}}{46080}+\cdots $$

An arithmetic sequence is given by \(b, \frac{2 b}{3}, \frac{b}{3}, 0, \ldots\) (a) State the sixth term. (b) State the \(k\) th term. (c) If the 20 th term has a value of 15 , find \(b\).

(a) Obtain a quadratic Maclaurin polynomial approximation, \(p_{2}(x)\), to \(f(x)=\cos 2 x\). (b) Compare the approximate value given by \(p_{2}(1)\) with actual value \(f(1)\).

The sum to infinity of a geometric sequence is four times the first term. Find the common ratio.

Find the sum of the first 40 positive integers.
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