![]() Note: The three dots (.) mean that this sequence is infinite. For example, all of the consecutive terms in the arithmetic sequence: This difference is called the common difference. Ĭlearly, this series is an A.P.An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. Thus, costs of digging a well for different lengths are 150, 170, 190, 210, …. I) The cost of digging a well for the first metre is $150 and rises by $20 for each succeeding metre.Ĭost of digging a well for the first meter ( a 1)=$150.Ĭost rises by $20 for each succeeding meterĬost of digging for the second meter ( a 2)=$150+$20=$170Ĭost of digging for the third meter ( a 3)=$170+$20=$210 Write down the first four terms with the following situation, will the terms be the first four terms of an arithmetic sequence? Therefore, the series of 7 prizes are as follows: If each prize is $20 less than its preceding prize, find the value of each of the prizes. A sum of $700 is to be used to give seven cash prizes to students of a school for their overall academic performance. The first three terms of this AP: a, a+ d, a+2 d=-13,-8,-3. Putting the value of d in equation (1), we get a=12-5(5)=-13. Let the first term of the AP = a and common difference = d According to first condition, a 4+ a 8=24Īccording to second condition, a 6+ a 10=44 The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Putting the value of d in equation (1), we get a+2(6)=16 Let the first term of the AP = a and common difference = d.ħth term exceeds the 5th term by 12, therefore a 7= a 5+12 Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12. Therefore, when d=3, the numbers are 5, 8, and 11 and when d=-3, the numbers are 11, 8, and 5. If the sum of three numbers in an A.P., is 24 and their product is 440, find the numbers. Hence, the required AP is 3, 4, 5, 6, 7, … Solving the pair of linear equations (1) and (2), we get a=3, d=1 Determine the AP whose 3rd term is 5 and the 7th term is 9. Then arithmetic progression is, a, a+ d, a+2 d, a+3 d, … We know that, if first term a and common difference d, then the arithmetic series is, a, a+ d, a+2 d, a+3 d, …. Write the arithmetic progressions write first term a and common difference d are as follows: So the first three terms of the sequence are-2, 3, 8. ī) Determine the values of the first three terms of the sequence.Ī) Since this is an arithmetic sequence, you can assume that there is a common difference between the terms. Given the arithmetic sequence 1- p, 2 p-3, p+5, …. Putting the value of a from equation (1), we get 38- d+5 d=-22⇒ d=-15 (iii) Here, a=5 and a 4=9½ to find: a 2 and a 3. Putting the value of d in equation (1), we get Putting the value of a from equation (1), we get (ii) Here, a 2=13 and a 4=3 to find a 1 and a 3. In the following APs, find the missing terms in the boxes: Write first four terms of the AP, when the first term a and the common difference d are given as follows: Find the common difference and write out the first 4 terms.Ĭommon difference=3 first 4 terms 8, 11, 14, 17Ĭommon difference=5 first 4 terms 3, 8, 13, 18Ĭommon difference=-4 first 4 terms -1,-5,-9,-16Ĭommon difference=-6 first 4 terms -2,-8,-14,-20 Question 2: show that each sequence is arithmetic. The sequence is to decrease, so choose a negative common difference for example, d=-3. The arithmetic sequence is:-7,-5,-3,-1, 1, …ī) Choose the first term for example, t 1=5. Keep adding the common difference until there are 5 terms. The sequence is to increase, so choose a positive common difference for example, d=2. Question 1: Writing an Arithmetic SequenceĪ) Choose any number as the first term for example, t 1=-7.
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