Find the sum of the first 40 terms of the arithmetic sequence 17, 24, 31, 38,...
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given the arithmetic sequence:
17, 24, 31, 38,.
Find the sum of the first 40 terms.
A1 = 17
d = 7
Formula for arithmetic sequence:
An = a1 + (n-1)d
Formula for the sum of arithmetic sequence.
Sn = ((a1 + an)/2)n
Solution:
Determine first the 40th terms in order to find the sum. To do so we will use the formula for the arithmetic sequence.
A40 = 17 + (40 -1 ) 7
A40 = 17 + (39) 7
A40 = 17 + 273
A40 = 290
Substitute the values of a1 and a40 to the formula for the sum of arithmetic sequence.
Sn = ((a1 + an)/2)n
Sn = ((17 + 290)/2)40
Sn= (153.5)40
Sn = 6140
Final answer:
Sn = 6140