Arithmetic and Geometric Sequences – ++ Prep

Arithmetic and Geometric Sequences

00:00 7 marks

An arithmetic sequence has first term \(8\) and common difference \(3\).

(a) Find the 15th term of the sequence. [2]

(b) Find the sum of the first 20 terms of the sequence. [2]

A geometric sequence has first term \(12\) and common ratio \(0.9\).

(c) Find the sum to infinity of this sequence. [3]

Part a

3 minutes 2 marks

Question

Find the 15th term of the sequence. [2]

Hint Hint

Hint

Use the arithmetic sequence formula: \(u_n = u_1 + (n-1)d\).

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation

Answer Answer

Complete Answer

\(50\)

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Part b

3 minutes 2 marks

Question

Find the sum of the first 20 terms of the sequence. [2]

Hint Hint

Hint

Use the sum formula: \(S_n = \frac{n}{2}[2u_1 + (n-1)d]\).

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation

Answer Answer

Complete Answer

\(730\)

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Part c

4 minutes 3 marks

Question

Find the sum to infinity of the geometric sequence. [3]

Hint Hint

Hint

Use the formula: \(S_\infty = \frac{u_1}{1-r}\) and verify that \(|r| < 1\).

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation

Answer Answer

Complete Answer

\(120\)

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Math Editor

Welcome Back!

Create your account

Build skills for today, tomorrow, and beyond. Education to future-proof your career.

By clicking "Sign in," you agree to our Terms of Use and our Privacy Policy

Hint: The password should be at least eight characters long. To make it stronger, use upper and lower case letters, numbers, and symbols like ! " ? $ % ^ & ).