Last updated at May 29, 2018 by Teachoo

Transcript

Example 13 How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78? AP is 24,21,18,โฆโฆโฆ Sum = ๐/2[2๐+(๐โ1)๐] Here, a = 24 d = 21 โ 24 = โ 3 Sum = Sn = 78 We have to find value of n Putting these values in equation Sum = ๐/2[2๐+(๐โ)๐] 78 = ๐/2[2ร24+(๐โ1)(โ3)] 78 ร2=๐[48+(๐โ1)(โ3)] 156 = n [ 48 โ 3n + 3] 156 = n [ 51 โ 3n] 156 = 51n โ 3n2 156 = 51n โ 3n2 3n2 โ 51n + 156 = 0 Dividing the equation by 3 3๐2/3โ51๐/3+156/3=0 n2 โ 17n + 52 = 0 We factorize by splitting the middle term n2 โ 13n โ 4n + 52 = 0 n (n โ 13) โ 4 (n โ 13) = 0 (n โ 13) (n โ 4) = 0 So, n = 13, n = 4 Since, both values are positive natural number. So either of them can be taken .

Finding number of terms given s

Chapter 5 Class 10 Arithmetic Progressions

Concept wise

- Checking if AP or not and finding a, d
- Finding nth term
- Finding n
- Finding AP
- Finding nth term from end
- Divisible/ multiples
- Statement questions - nth term
- Finding sum of n terms
- Finding number of terms given s
- Given nth term finding s
- Statement questions - Sum of n terms
- Determining AP and finding sum

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.