Question

What is the 101st term for the sequence 13, 9, 5, 1... ?

Answer 1

Explanation:

• a=13
• d=13-9=4

`{:}\longrightarrow`
`\sf S_n={\frac {n}{2}}\left [2a-(a-1)d\right]`

`{:}\longrightarrow`
`\sf S_101={\frac {101}{2}}\left [26 (12)4\right]`

`{:}\longrightarrow`
`\sf 50.5×1248`

`{:}\longrightarrow`
`\sf S_101=63504`

• 
  `{:}\longrightarrow`
  `\sf a_n=a+(n-1)d`

`{:}\longrightarrow`
`\sf a_101=13+(101-1)-4`

`{:}\longrightarrow`
`\sf a_101=13+100(-4)`

`{:}\longrightarrow`
`\sf 13-400`

`{:}\longrightarrow`
`\sf a_101=-387`