the first 4 terms of an arithmetic are x,9,3x,3x+y find the sum of first 100 terms of this sequence [closed]
Solution 1:
Start by taking the first four terms $(x, 9, 3x, 3x+y)$ and finding the value of x that makes the sequence arithmetic. $$9-x=3x-9$$ $$x=\frac{9}{2}$$
Now we see that the common difference is $\frac{9}{2}$. The sum of the first 100 terms is $$\sum_{n=1}^{100} \frac{9}{2}n=22,725$$