Find the 21st term of an arithmetic sequence with terms a_6=50 and a_11=85

fofopausiomiava

fofopausiomiava

Answered question

2022-10-10

Find the 21st term of an arithmetic sequence with terms a 6 = 50 and a 11 = 85

Answer & Explanation

Garrett Valenzuela

Garrett Valenzuela

Beginner2022-10-11Added 9 answers

If m t h term of an arithmetic series is a m and n t h term of same series is a n , then common difference is given by
a m - a n m - n
As a 6 = 50 and a 11 = 85
d = 85 - 50 11 - 6 = 35 5 = 7
and as a 6 = a 1 + ( 6 - 1 ) d
we have 50 = a 1 + 5 × 7
or a 1 = 50 - 35 = 15
and a 21 = a 1 + ( 21 - 1 ) d
= 15 + 20 × 7 = 15 + 140 = 155

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