Question

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

Answer 1

Step-by-step explanation:

• a=13
• d=13-9=4

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

${:}\longrightarrow$$\sf S_101={\dfrac {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$