Write an expression for the apparent nth term of the sequence.(Assume that n beg

Question

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1) 1, 1/4, 1/9, 1/16, 1/25,... I have a hard time noticing the algebraic patterns needed toslove these so would there be an easier way to solve thenrecognizing what happens to each term in the sequence? Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1) 1, 1/4, 1/9, 1/16, 1/25,... I have a hard time noticing the algebraic patterns needed toslove these so would there be an easier way to solve thenrecognizing what happens to each term in the sequence?

Explanation / Answer

There's not really an easier way to write theexpression. Maybe instead of just looking at the numbersyou're given, try and manipulate them all the same way and see ifyou can notice anything after that. For example, your problemis: 1, 1/4, 1/9, 1/16, 1/25, ..... 1 divided by 1 is still one. Rewrite the sequence likethis first: 1/1, 1/4, 1/9, 1/16, 1/25, ...... Now, since all of the numerators here are one, you cannotreally do anything to them. However, the denominators ofthese numbers is obviously what's changing. Since we caneasily see that, the easiest way to try and rewrite those numbersis to factor them. 1/1 = 1/ 1*1 1/4 = 1/2*2 1/9 = 1/3*3 1/16 = 1/4*4 1/25 = 1/5*5 Now that you've rewritten the denominators it's a lot easierto figure out what's going on here. Any number multipliedwith itself is said to be squared, right? Rewrite thedenominators as squares and you can see what the general expressionwould be. nth term = 1 /n2

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.