How to find Arithmetic Sequences?

Question

Find t1 from the following A.P. 4,9,14,....

Answer 1

All arithmetic sequences take the form a, a+d, a+2d, a+3d, ... where a is the first term (t₁) and d the common difference.

In this case t₁=a=4, and d=9-4=5. t_n=a+(n-1)d=4+5(n-1)=4+5n-5=5n-1.

So t₂=5×2-1=9, t₃=5×3-1=14, etc.