Question

write the next three numbers in the sequence below
13, 23, 33, 43, 53, \boxed{ }, \boxed{ }, \boxed{ }
what is the common difference for the sequence listed below.
common difference = \boxed{ }
write the function formula for the sequence
t(n) = \boxed{ }
what is t(60) = \boxed{ }
when is t(n) = 1193
\boxed{ }
question help: message instructor

Explanation:

Part 1: Next three numbers in the sequence

Step1: Identify the pattern

The sequence is \( 13, 23, 33, 43, 53, \dots \). Each term increases by 10.

Step2: Calculate the next terms

• 6th term: \( 53 + 10 = 63 \)
• 7th term: \( 63 + 10 = 73 \)
• 8th term: \( 73 + 10 = 83 \)

Part 2: Common difference

Step1: Define common difference

For an arithmetic sequence, common difference \( d = \text{term}_n - \text{term}_{n-1} \).

Step2: Calculate \( d \)

Take \( 23 - 13 = 10 \), or \( 33 - 23 = 10 \), etc. So \( d = 10 \).

Part 3: Function formula for the sequence

Step1: Recall arithmetic sequence formula

The formula for the \( n \)-th term of an arithmetic sequence is \( t(n) = t(1) + (n - 1)d \), where \( t(1) \) is the first term and \( d \) is the common difference.

Step2: Substitute values

Here, \( t(1) = 13 \) and \( d = 10 \). So:
\( t(n) = 13 + (n - 1) \times 10 \)
Simplify: \( t(n) = 13 + 10n - 10 = 10n + 3 \).

Part 4: Find \( t(60) \)

Answer:

s:

• Next three numbers: \( 63, 73, 83 \)
• Common Difference: \( 10 \)
• Function formula: \( t(n) = 10n + 3 \)
• \( t(60) = 603 \)
• \( n \) when \( t(n) = 1193 \): \( 119 \)