C1 Sequences and series

Can someone help me with this exam question . I wanted to have an attempt before looking at the answer but have completely forgot how to do this

In the arithmetic series $k+2k+3k....+100$
k is a positive integer and k is a factor of 100
i). Find in terms of k, an expression for the number of terms in this series

ii). Show that the sum of this series is $50+\frac{5000}{k}$

No idea on how to start my head has gone blank . A bit of guidance would be appreciated thanks

Can someone help me with this exam question . I wanted to have an attempt before looking at the answer but have completely forgot how to do this

In the arithmetic series $k+2k+3k....+100$
k is a positive integer and k is a factor of 100
i). Find in terms of k, an expression for the number of terms in this series

ii). Show that the sum of this series is $50+\frac{5000}{k}$

No idea on how to start my head has gone blank . A bit of guidance would be appreciated thanks

The nth term is $u_n = a + (n-1)d$In this case $100 = k + (n-1)k$Rearrange and solve for k.For ii) Note that $S_n = \frac{n}{2}(a+l)$

Thanks for the reply. I have done the first part and got $\frac{100}{k}$.Having a few problems with the second part What I did was half the $a+l$ part first.So I got $\frac{100}{k}(\frac{k}{2}+50)$Expanding I got $50k+5000$Is the 100 supposed to be 100k or have I made an error with my algebra

Try expanding that again more carefully.