If S = (n)/(2)(a + L), find n when, S= 640, a = 25 and L = 39

Question

If S =
`(n)/(2)`(a + L), find n when, S= 640, a = 25 and L = 39

Answer 1

n = 20

Explanation:

Sum of an arithmetic series

`S_n=(n)/(2)(a+l)`

where:

• a = first term
• l = last term
• n = number of terms

Given:

• 
  `S_n=640`
• 
  `a=25`
• 
  `l=39`

Substituting the given values into the formula and solving for n:

`\implies 640=(n)/(2)(25+39)`

`\implies 640 \cdot 2=n(25+39)`

`\implies 1280=n(25+39)`

`\implies 1280=64n`

`\implies n=(1280)/(64)`

`\implies n=20`