NCERT Class 10 Mathematics

96 MATHEMATICS Let us denote the first term of an AP by a 1 , second term by a 2 ,.. ., nth term by an and the common difference ...

ARITHMETIC PROGRESSIONS 97 Similarly, when a = – 7, d = – 2, the AP is – 7, – 9, – 11, – 13,... a = 1.0, d = 0.1, the AP is 1.0, ...

98 MATHEMATICS Note that to find d in the AP : 6, 3, 0, – 3,.. ., we have subtracted 6 from 3 and not 3 from 6, i.e., we should ...

ARITHMETIC PROGRESSIONS 99 (iv)a 2 – a 1 = 1 – 1 = 0 a 3 – a 2 = 1 – 1 = 0 a 4 – a 3 = 2 – 1 = 1 Here, a 2 – a 1 = a 3 – a 2 a ...

100 MATHEMATICS (ix) 1, 3, 9, 27,... (x)a, 2 a, 3a, 4 a,... (xi) a, a^2 , a^3 , a^4 ,... (xii) 2, 8, 18, 32,... (xiii) 3, 6, 9, ...

ARITHMETIC PROGRESSIONS 101 Now, looking at the pattern formed above, can you find her monthly salary for the 6th year? The 15th ...

102 MATHEMATICS an is also called the general term of the AP. If there are m terms in the AP, then am represents the last term w ...

ARITHMETIC PROGRESSIONS 103 Example 6 : Check whether 301 is a term of the list of numbers 5, 11, 17, 23,... Solution : We have ...

104 MATHEMATICS To find the 11th term from the last term, we will find the total number of terms in the AP. So, – 62 = 10 + (n – ...

ARITHMETIC PROGRESSIONS 105 It is an AP as the difference between the consecutive terms in the list is 80, i.e., d = 80. Also, a ...

106 MATHEMATICS Choose the correct choice in the following and justify : (i) 30th term of the AP: 10, 7, 4,... , is (A) 97 (B) ...

ARITHMETIC PROGRESSIONS 107 Find the 20th term from the last term of the AP : 3, 8, 13,.. ., 253. The sum of the 4th and 8th te ...

108 MATHEMATICS We will now use the same technique to find the sum of the first n terms of an AP : a, a + d, a + 2d,... The nth ...

ARITHMETIC PROGRESSIONS 109 Here, a = 100, d = 50 andn = 21. Using the formula : S = 2(1)✁ 2 n an d✂ ✄ , we have S = ☎ ✆ 21 2 10 ...

110 MATHEMATICS i.e., 910 = 91d or, d =10 Therefore, a 20 = 10 + (20 – 1) × 10 = 200, i.e. 20th term is 200. Example 13 : How ma ...

ARITHMETIC PROGRESSIONS 111 Therefore, Sn = (1 ) 2 nn or Sn = (1) 2 nn So, the sum of first n positive integers is given by Sn = ...

112 MATHEMATICS or, a + 2d = 600 and a + 6 d = 700 Solving these equations, we getd = 25 and a = 550. Therefore, production of T ...

ARITHMETIC PROGRESSIONS 113 How many terms of the AP : 9, 17, 25,... must be taken to give a sum of 636? The first term of an A ...

114 MATHEMATICS Fig. 5.4 [Hint : Length of successive semicircles is l 1 , l 2 , l 3 , l 4 ,... with centres at A, B, A, B,.. ., ...

ARITHMETIC PROGRESSIONS 115 EXERCISE 5.4 (Optional)* Which term of the AP : 121, 117, 113,.. ., is its first negative term? [Hi ...