Answer:
smallest integer=9,
total number of integers are in the sequence = 19.
Step-by-step explanation:
- let a be the first term and the number of terms be n. as they are consecutive,the common difference will be 1. these will form Arithmetic Progression series.
- the sum of n terms in AP series is :
[ where, l: last term]
- or, sum of n terms in AP series is :
[where, d: common difference]
using the first formula,
342 =
342=
342=2an .......equation 1.
using the second formula,
342=
684=n[2a+n-1]
684=2an+n^2-n
from equation 1,
342=n^2-n .......equation 1
-n-342=0
after solving, the solution to the above equation is 19.
substituting this in equation 2,
171=a[19]
a=9
so, smallest integer= a = 9,
total number of integers are in the sequence = n = 19.