Arithmetic Series www mathsrevision com Adv Higher nth

Arithmetic Series An Arithmetic Series is a sequence which differs by the same amount

Arithmetic Series Example : Find a formula for the nth term of the sequence

Arithmetic Series The sum of an Arithmetic Series Rewriting the terms in reverse Now

Arithmetic Series For a infinite number of terms then a = first term l

Arithmetic Series Example : For 2 + 5 + 8 + 11 +. .

Arithmetic Series Example : If the first term is 37 and difference is -4.

Arithmetic Series Example : Find the number of terms in the series 5 +

Arithmetic Series Example : Find the sum of 2 + 4 + 6 +

Arithmetic Series Example : The second term of an Arith. sequence is 18 and

Arithmetic Series Exercise 1 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Geometric Series A Geometric sequence is one in which the ratio of each term

Sum of Geometric Series Let Sn denote the sum of n terms, a the

Sum of Geometric Series Find u 10 for the Geometric Sequence : - 144,

Sum of Geometric Series Find S 19 for the Geometric Sequence : - 3,

Sum of Geometric Series A Geometric Series has the first term 27 and common

Sum of Geometric Series Given find Sub into 29 -Jan-22 Created by Mr. Lafferty

Arithmetic Series Exercise 2 A 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Maclaurin’s Theorem Expansions You need to learn the basic expansions 29 -Jan-22 Created by

Maclaurin’s Theorem Expansions We can combine expansions to more complicated functions. Expand 29 -Jan-22

Maclaurin’s Theorem Expansions Expand up to the power of x 4 etc. . .

Trick ! Maclaurin’s Theorem ( 1 + cosx - 1 ) Expansions Expand up

Maclaurin’s Theorem Expansions Expand 29 -Jan-22 up to the power of x 6 Created

Arithmetic Series Exercise 2 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

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Arithmetic Series www. mathsrevision. com Adv. Higher nth term & Sum of Arithmetic Series nth and sum of Geometric Series Maclaurin’s Expansion 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series An Arithmetic Series is a sequence which differs by the same amount each time Let the first term be a and the difference be d then 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Example : Find a formula for the nth term of the sequence 9, 12, 15, . . . and the 20 th term. a=9 d = 12 - 9 = 3 u 20 = 3(20) + 6 un = a + (n – 1)d u 20 = 60 + 6 un = 9 + 3(n – 1) u 20 = 66 un = 3 n + 6 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series The sum of an Arithmetic Series Rewriting the terms in reverse Now adding each corresponding terms 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series For a infinite number of terms then a = first term l = last term 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Example : For 2 + 5 + 8 + 11 +. . . Find u 15 and S 8. a=2 d=3 un = 2 + 3(n – 1) un = 3 n – 1 S 8 = 100 u 15 = 3(15) - 1 = 44 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Example : If the first term is 37 and difference is -4. Find u 15 and S 8. un = a + (n – 1)d u 15 = 37 - 4(15 – 1) u 15 = -19 29 -Jan-22 S 8 = 184 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Example : Find the number of terms in the series 5 + 8 + 11. . . + 62. a=5 d=3 un = a + (n – 1)d 5 + 3(n – 1) = 62 3 n + 2 = 62 n = 20 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Example : Find the sum of 2 + 4 + 6 + 8. . + 146 a=2 d=2 un = a + (n – 1)d 2 + 2(n – 1) = 146 2 n = 146 n = 73 29 -Jan-22 S 8 = 5402 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Example : The second term of an Arith. sequence is 18 and fifth is 21. Find the common difference, first term and sum of the first 10 terms un = a + (n – 1)d (u 2) a + d = 18 (u 5) a + 4 d = 21 d=1 a = 17 29 -Jan-22 S 10 = 215 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Exercise 1 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Geometric Series A Geometric sequence is one in which the ratio of each term to the previous is a constant called the common ratio (r) 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series Let Sn denote the sum of n terms, a the first term and r the common ratio. If r > 1 better to use 29 -Jan-22 Created by Mr. Lafferty Maths Dept. r≠ 1

Sum of Geometric Series Find u 10 for the Geometric Sequence : - 144, 108, 81, 60¾ 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series Find S 19 for the Geometric Sequence : - 3, -6, 12, -24. . . 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series A Geometric Series has the first term 27 and common ratio Take logs Find the least number of terms the series can have if its sum exceeds 550. 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Sum of Geometric Series Given find Sub into 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Exercise 2 A 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Maclaurin’s Theorem Expansions You need to learn the basic expansions 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Maclaurin’s Theorem Expansions We can combine expansions to more complicated functions. Expand 29 -Jan-22 up to the power of x 4 Created by Mr. Lafferty Maths Dept.

Maclaurin’s Theorem Expansions Expand up to the power of x 4 etc. . . 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Trick ! Maclaurin’s Theorem ( 1 + cosx - 1 ) Expansions Expand up to the power of x 6 But Now sub into ln(1 + x) 29 -Jan-22 Created by Mr. Lafferty Maths Dept.

Maclaurin’s Theorem Expansions Expand 29 -Jan-22 up to the power of x 6 Created by Mr. Lafferty Maths Dept.

Arithmetic Series Exercise 2 29 -Jan-22 Created by Mr. Lafferty Maths Dept.