Question
Find the sum of the first 50 terms of the given sequence: 4, 9, 14, 19, 24, \dots
Find the sum of the first 50 terms of the given sequence: 4, 9, 14, 19, 24, \dots
The difference between any given two successive terms is 5. So the sequence is an arithmetic progression.
a_1=4 and d=5
a_n=a_1+(n-1)d
=4+5(n-1)
=5n-1
Therefore, the general term of the sequence is a_n=5n−1. To calculate the 50^{th} partial sum of this sequence we need the 1st and the 50th terms:
a_1=4
a_{50}=5\times 50-1=249
Next use the formula to determine the 50^{th} partial sum of the given arithmetic sequence.
S_{50} = \dfrac{50(a_1+a_{50})}{2} =\dfrac{50(4+249)}{2}=6325
\therefore S_{50}=6325