Question

How many numbers are there in the series of 2-20 if the sum is 143

Answer 1

Answer:

11

Step-by-step explanation:

let number of terms between 2 and 20 = n

so, total number of terms including 2 and 20 = n+2

1st term = a = 2

last term = b = 20

common difference = d = (b-a)/(n+1) = (20-2)/(n+1) = 18/(n+1)

sum of n terms = n{2a+(n-1)d}/2

given, sum of all terms is 143

=> sum of (n+2) terms is 143

=> (n+2){2a+(n+2-1)d}/2 = 143

=> (n+2){2×2+(n+1)18/(n+1)} = 143×2

=> (n+2){4+18} = 286

=> (n+2)×22 = 286

=> n+2 = 286/22 = 13

=> n = 13-2 = 11