Smallest two digit odd number = 11
Largest two digit odd number = 99
Difference between consecutive odd numbers = 2
∴The sequence is 11,13,....,99
The number of terms in the given AP is
an=a+(n−1)d
⇒99=11+(n−1)2
⇒(n−1)2=88
⇒n−1=44
⇒n=45
Sum of two digit odd numbers is,
Sn=n2[2a+(n−1)d]
⇒452[2(11)+(45−1)2]
⇒452[22+88]
⇒45[55]=2475