Question

Find a^n for the arithmetic series

S^16=856 and a^1 =76

Answer 1

`a_(n)` = - 3n + 79

Explanation:

the nth term of an arithmetic series is

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 76 and we have to find d

the sum to n terms of an arithmetic series is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

given S₁₆ = 856 , then

`(16)/(2)` [ (2 × 76 ) + 15d ] = 856

8(152 + 15d) = 856 ( divide both sides by 8 )

152 + 15d = 107 ( subtract 152 from both sides )

15d = - 45 ( divide both sides by 15 )

d = - 3

Then

`a_(n)` = 76 - 3(n - 1) = 76 - 3n + 3 = - 3n + 79