Find the sum of the arithmetic sequence 174, 168, 162 …, if there are 37 terms

Stacy Barr

Stacy Barr

Answered question

2022-09-25

Find the sum of the arithmetic sequence 174, 168, 162 …, if there are 37 terms

Answer & Explanation

Kelbelol

Kelbelol

Beginner2022-09-26Added 10 answers

Sum of an Arithmetic series
{ a , ( a + d ) , ( a + 2 d ) , ... ( a + ( n - 1 ) d ) } up to n terms is given by
n 2 × ( 2 a + ( n - 1 ) d )
where a is the first term and d is the difference between a term and its preceding term.
Here first term a=174 and d=168−174=−6 and n=37
Hence the desired sum is 37 2 × { 2 × 174 + ( 37 - 1 ) × ( - 6 ) } or
37 2 × ( 348 - 36 × 6 ) or 37 2 × ( 348 - 216 ) or
37 2 × 132 = 2442

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