Unlock Any Sequence Term

Imagine being asked for the fiftieth term of a sequence. Writing out fifty numbers would take ages. But with a term rule, you can leap straight to the answer... like unlocking a secret door! You only need the term's position and one reliable calculation.

A term rule might say: three times n, plus two. The letter n means the term NUMBER. So, for the first term, n is one. For the second term, n is two. For the tenth term, n is ten. The named position tells you exactly what to put in. Suppose you want the fourth term. Replace n with four. Now the rule becomes three times four, plus two. Multiply first: three times four is twelve. Then add two. The fourth term is fourteen. Position in... term out. Neat and dependable. Watch out for a sneaky mistake. Three n means three TIMES n, not three plus n. And n is the position, not the value of the previous term. If you need the eighth term, substitute eight straight into the rule. Do not build your way along the sequence.

Now try a full question. A sequence has the term rule: five times n, minus two. Find the fourteenth term. First, spot the named position. We need term fourteen, so n equals fourteen. That substitution is the crucial first step. Replace n with fourteen. You now have five times fourteen, minus two. Multiplication comes first. Five times fourteen is seventy. Keep the minus two visible - do not lose that final part of the rule. Seventy minus two equals sixty-eight. So, the fourteenth term is sixty-eight. Notice the two different jobs: fourteen was the POSITION you put into the rule. Sixty-eight is the VALUE that came out. Keeping those labels separate helps you avoid swapping them in a hurry.

Remember: take the named term number, substitute it for n, then follow the rule carefully. Multiply before you add or subtract. Position in... term out. With that simple routine, even the hundredth term is completely within your reach!