The sum of all natural numbers from 75 to 97 is:

$$t_{n}$$=a+(n-1)d where
$$t_{n}=n^{th}$$ term,
a= first term
n=no. of terms
d= difference between terms

Here $$t_{n}$$= 97,a=74,d=1
97=74+(n-1)1
$$\Rightarrow$$97=73+n
$$\Rightarrow$$ n=23

Sum of natural numbers between 74 and 97 is
$$S_{n}$$=$$\frac{n}{2}$$[2a+(n-1)d]

Here n=23, a=74, d=1

$$S_{n}$$=$$\frac{23}{2}$$[74+(23-1)1]

        = $$\frac{23}{2}\times172$$=$$23\times86$$=1978

$$\therefore$$ Sum of natural numbers between 74 and 97 is 1978