Question #f78de

1 Answer
Jan 8, 2018

Sum of the numbers is #361#

Explanation:

The A.P series is #{1,3,5,7 ....35,37}#

First term of consecutive odd numbers of A.P series is #a_1=1#

Last term of consecutive odd numbers of A.P , series is #a_n=37#

Common difference is #d= 3-1=2#

We know #n# th term is #a_n=a_1+(n-1)d # or

#37= 1+(n-1)*2 or (n-1)*2=37-1# or

# (n-1)*2=36 or n-1=36/2 =18 :. n=19#. Therefore

Number of terms is #n=19# .Average of first and last term

is # a_m=(1+37)/2=19 :. S_n= a_m*n=19*19=361# . Hence

sum of the numbers is #S_n=361# [Ans]