Question

Determine the number of terms n in each arithmetic series.
a1= 17 , d= 10 , Sn= 513

Answer 1

Answer: The Number of terms is 9.

Explanation:

The formula for the sum of an AP is ,Sn =
`(n)/(2)`
`(`
`2a+(n-1)d)`

Given a1=17 , d = 10 , Sn = 513

Putting the values,

513 =
`(n)/(2)`
`(`
`2*17+(n-1)*10)`

1026 = 17n + 17n + 10
`n^(2)` - 10n

10
`n^(2)` + 24n - 1026 =0

Therefore n = 9.