Question

He 5th term of a linear sequence is 19, the 6th term of the sequence is 25, what is the 100th term

Answer 1

To find the 100th term of a linear sequence when the 5th term is 19 and the 6th term is 25, we calculate the common difference and use it along with the nth term formula. The common difference is 6, and the 100th term calculates to be 589.

Step-by-step explanation:

The question is related to a linear sequence. To find the 100th term, we need to determine the common difference and use the nth term formula of an arithmetic progression, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the term number.

Given the 5th term (a5) is 19 and the 6th term (a6) is 25, we find the common difference by subtracting the 5th term from the 6th term:

• d = a6 - a5 = 25 - 19 = 6

Now to find the 100th term (a100), we plug in the values into the nth term formula:

• a100 = a1 + (100 - 1)d

But first, we need to find the first term (a1). Using the 5th term formula, we have:

• 19 = a1 + (5 - 1)6
• 19 = a1 + 24
• a1 = 19 - 24
• a1 = -5

Now we can find the 100th term:

• a100 = -5 + (100 - 1)6
• a100 = -5 + 99 * 6
• a100 = -5 + 594
• a100 = 589

So the 100th term of the sequence is 589.