Topicm70c74aa98941ac47_1528449000663_0Topic

The sum of the terms of the arithmetic sequencesequencesequence

Levelm70c74aa98941ac47_1528449084556_0Level

Third

Core curriculumm70c74aa98941ac47_1528449076687_0Core curriculum

VI. Sequences. Student:

4) checks if a given sequence is arithmetic or geometric;

5) applies the formula for the nth term and for the sum of n first terms of the arithmetic sequencearithmetic sequencearithmetic sequence.

Timingm70c74aa98941ac47_1528449068082_0Timing

45 minutes

General objectivem70c74aa98941ac47_1528449523725_0General objective

To interpret and correctly use the information presented both in the mathematics oriented and general knowledge texts, as well as in the form of diagrams, graphs and tables.

Specific objectivesm70c74aa98941ac47_1528449552113_0Specific objectives

1. To develop English language skills, mathematical, IT, general knowledge, cience competences master the ability of learning and self‑development.

2. To get to know the formula for the sum of n initial terms of the arithmetical sequencesequencesequence.

3. To apply the formula to the sum of n initial terms of the arithmetical sequence.

Learning outcomesm70c74aa98941ac47_1528450430307_0Learning outcomes

The student:

- learns the formula for the sum of n initial terms of the arithmetic sequencearithmetic sequencearithmetic sequence,

- applies the formula to the sum of n initial terms of the arithmetical sequence.

Methodsm70c74aa98941ac47_1528449534267_0Methods

1. Station teaching method.

2. Case studies.

Forms of workm70c74aa98941ac47_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm70c74aa98941ac47_1528450127855_0Introduction

Students, working in two groups, calculate the sum of consecutive terms of given arithmetic sequences.

Station 1 – students calculate the sum of 10 natural numbers, which divided by 5 give the remainder 1 (let’s assume aIndeks dolny 1₁ = 1).

Answer: 235.

Station 2 - students calculate the sum: 2 + 4 + 6 + ... + 50.

Answer: 650.

Students present the results of their calculations and the way in which they calculated them.

Procedurem70c74aa98941ac47_1528446435040_0Procedure

Students analyse Interactive illustration on their own.

Task 1

Analyse the material contained in the Interactive illustration carefully.

[Interactive illustration]

Formulate appropriate conclusions.

Conclusion:

The sum of n initial terms of the arithmetic sequencesequencesequence is equal to the arithmetic mean of the first and last terms multiplied by the number of terms of the sequenceterms of the sequenceterms of the sequence.

The teacher writes down the conclusion formulated by the students in the form of a theorem.

Theorem - on the sum of the terms of the arithmetical sequence:

The sum of $S_n$ of the initial n terms of the arithmetic sequence $a_n$ is equal:

Using the theorem learnt students solve the tasks.

Task 2

In arithmetic sequence (aIndeks dolny n_n): aIndeks dolny 1₁ = 5, r = 4.

How many terms of this sequence give a total of 780?

Answer: 26.

Task 3

In arithmetic sequence (aIndeks dolny n_n): aIndeks dolny 1₁ = 5, r = -2

Calculate the sum of the terms of this sequence from the tenth to the twentieth (inclusive).

Answer: -253.

Task 4

How many numbers do you have to insert between 20 and 254 to get an arithmetic sequence, whose sum is 2055?m70c74aa98941ac47_1527752263647_0How many numbers do you have to insert between 20 and 254 to get an arithmetic sequence, whose sum is 2055?

Answer: 13 numbers.

An extra task

Solve the equation 2 + 4 +6 + ... + 2(x + 1) = 650 for x > 0 whose left side is the sum of consecutive terms of the arithmetic sequencesequencesequence.

Answer: x = 24.

Lesson summarym70c74aa98941ac47_1528450119332_0Lesson summary

Students do revision exercises.

Together, they formulate a conclusion to remember.

- The sum of n initial terms of the arithmetic sequence is equal to the arithmetic mean of the first and last terms multiplied by the number of terms of the sequence.m70c74aa98941ac47_1527752256679_0- The sum of n initial terms of the arithmetic sequence is equal to the arithmetic mean of the first and last terms multiplied by the number of terms of the sequence.

Selected words and expressions used in the lesson plan

sequencesequencesequence

arithmetic sequencearithmetic sequencearithmetic sequence

terms of the sequenceterms of the sequenceterms of the sequence

sum of arithmetic sequencesum of arithmetic sequencesum of arithmetic sequence

initial terms of the sequenceinitial terms of the sequenceinitial terms of the sequence

difference of arithmetic sequencedifference of arithmetic sequencedifference of arithmetic sequence

nIndeks górny th^th term of the sequencenIndeks górny th^th term of the sequencenIndeks górny th^th term of the sequence