Example 5 Find the sum of the first 10 terms of the arithmetic sequence 5. 9. 13. 17. Formula: S = (a + an) or Sn = ar 12a a1 + (n-1)] n = number of terms added together a = first term in sequence d = common difference 10 Solution Sio = 2 (265) + (10 - 1)41 Sio = 5[10+ (94) Sio = 5110 + 36 Sto = 5(46)
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Answer:
230
Step-by-step explanation:
Before we find the sum of the first 10 terms of the arithmetic sequence {5, 9, 12, 17, ...}, let's find first the common difference and the 10th term of the sequence.
d = =
Use the formula:
We are looking for the sum of the first 10 terms so n = 10.
5 is the first term.
180 is the tenth term.
So, 230 is the sum of the first 10 terms of the arithmetic sequence.
FOR CHECKING:
Put all the terms here from 1 to 10 terms.
{ 5, 9, 13, 17, 21, 25, 29, 33, 37, 41 }