Find the explicit formula for the following sequence 10, 12.5, 15, 17.5,...

Darius Miles

Darius Miles

Answered question

2022-09-24

Find the explicit formula for the following sequence 10, 12.5, 15, 17.5,...

Answer & Explanation

ruinsraidy4

ruinsraidy4

Beginner2022-09-25Added 17 answers

The sequence 10,12.5,15,17.5,... is arithmetic sequence with first term a=10 and common difference d = 12.5 - 10 = 2 , 5
In an arithmetic sequence { a , a + d , a + 2 d , a + 3 d , ... ... . }
n t h term is given by
a + ( n - 1 ) d = 10 + ( n - 1 ) 2.5 = 10 + 2.5 n - 2.5 = ( 7.5 + 2.5 n )
Sum of the series up to n t h term is given by
n 2 ( 2 a + ( n - 1 ) d ) = n 2 ( 2 10 + ( n - 1 ) 2.5 or
n 2 ( 20 + 2.5 n - 2.5 ) or n 2 ( 17.5 + 2.5 n )

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