A sequence starts at 10 . The term-to-term rule is to subtract 3 then multiply by 2 each time. a) Work out the fourth term of the sequence. b) Is this sequence increasing, decreasing or neither?

Start at 10: The sequence starts at 10, and the term-to-term rule is to subtract 3 and then multiply by 2. To find the first term after the initial value, we apply the rule to the starting number. First term (starting value): 10 Second term calculation: (10 - 3) * 2Calculate second term: Now we calculate the second term using the term-to-term rule. Second term: (10 - 3) * 2 = 7 * 2 = 14Find third term: Next, we apply the term-to-term rule to the second term to find the third term. Third term calculation: (14 - 3) * 2Calculate fourth term: We calculate the third term. Third term: (14 - 3) * 2 = 11 * 2 = 22Determine sequence pattern: We apply the term-to-term rule to the third term to find the fourth term. Fourth term calculation: (22 - 3) * 2We calculate the fourth term. Fourth term: (22 - 3) * 2 = 19 * 2 = 38To determine if the sequence is increasing, decreasing, or neither, we observe the pattern of the terms. We started with 10, then the sequence went to 14, 22, and 38. Each term is larger than the previous term, which indicates the sequence is increasing.

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Math Problems

Grade 8

Interpreting Linear Expressions

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Q. A sequence starts at

10

. The term-to-term rule is to subtract

3

then multiply by

2

each time.

\newline

a) Work out the fourth term of the sequence.

\newline

b) Is this sequence increasing, decreasing or neither?

Start at $10$ : The sequence starts at $10$ , and the term-to-term rule is to subtract $3$ and then multiply by $2$ . To find the first term after the initial value, we apply the rule to the starting number. $\newline$ First term (starting value): $10$ $\newline$ Second term calculation: $(10 - 3) \times 2$
Calculate second term: Now we calculate the second term using the term-to-term rule. $\newline$ Second term: $(10 - 3) \times 2 = 7 \times 2 = 14$
Find third term: Next, we apply the term-to-term rule to the second term to find the third term. $\newline$ Third term calculation: $(14 - 3) \times 2$
Calculate fourth term: We calculate the third term. $\newline$ Third term: $(14 - 3) \times 2 = 11 \times 2 = 22$
Determine sequence pattern: We apply the term-to-term rule to the third term to find the fourth term. $\newline$ Fourth term calculation: $(22 - 3) \times 2$
Determine sequence pattern: We apply the term-to-term rule to the third term to find the fourth term. $\newline$ Fourth term calculation: $(22 - 3) \times 2$ We calculate the fourth term. $\newline$ Fourth term: $(22 - 3) \times 2 = 19 \times 2 = 38$
Determine sequence pattern: We apply the term-to-term rule to the third term to find the fourth term. $\newline$ Fourth term calculation: $(22 - 3) \times 2$ We calculate the fourth term. $\newline$ Fourth term: $(22 - 3) \times 2 = 19 \times 2 = 38$ To determine if the sequence is increasing, decreasing, or neither, we observe the pattern of the terms. We started with $10$ , then the sequence went to $14$ , $22$ , and $38$ . Each term is larger than the previous term, which indicates the sequence is increasing.