The tenth term of an arithmetic progression is equal to twice the fourth term. The twentieth term of the progression is 44.
(i) Find the first term and the common difference.
(ii) Find the sum of the first 50 terms.
The formula for Arithmetic Progression is
where = the rth term, a = the first term and d = the common difference
Now the tenth term is equal to twice the fourth term in this arithmetic progression
Now the 20th term or
Substituting , we get or or
the first term a=6, and the common difference d=2
The formula for Sum of Arithmetic Progression is
the sum of the first 50th term is = 2750