Let the five numbers which form arithmetic sequence be a-2d,a-d,a,a+d,a+2d where a is the first term and d is common difference.
Mean of these 5 numbers= 18
→ a-2d+a-d+a+a+d+a+2d = 5×18
→ 5 a= 5×18
Dividing both side by 5, we get , →a = 18
It is also given Mean of the squares of the five numbers is 374.
(a- 2 d)² + (a- d)² + a² +(a +d )² +(a+ 2 d)² = 5 × 374
→ a² + 4 d²- 4 ad +a² +d² -2 a d +a² +a² +d² +2 a d+a² + 4 d²+ 4 ad =5 × 374
→ 5 a² + 10 d²=5 × 374
→ 5 × (a² + 2 d²)=5 × 374
Dividing both sides by 5,we get
a² + 2 d²= 374
As , a=18, Substituting the value of a in above equation
→18² + 2 d²=374
→324 + 2 d²=374
→ 2 d² = 374 -324
→ 2 d²=50
Dividing both side by 2, we get
→ d²= 25
→ d² =5²
→ d = 5
The five numbers are, 18-2×5, 18 -5,18,18+5, 18 +2×5 ,= 8, 13, 18, 23, 28.
So, greatest number among these 5 numbers are 28.