Question

The start of an arithmetic sequence is

5,
13,
21,
One of the terms in the sequence has a value of 621.
At what position in the sequence is this term?

Answer 1

The general formula for the terms of an arithmetic sequence is given by:an

a1 + (n - 1) * d

an is the n-th term of the sequence,

a1 is the first term of the sequence,

n is the position of the term in the sequence,

d is the common difference between successive terms.

For example, the first term (a1) is 5, and there is a constant difference of 8 between successive terms (13 - 5 = 8, 21 - 13 = 8,

we can use this formula to find the position (n) of the term with a value of 621 :

621 = 5 + (n - 1)× 8

621 = 5+8n-8

621 = -3+8n

621+3=8n

624 = 8n

n=624/8 =78

the term with a value of 621 is located at position 78 in the sequence.

Explanation: