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Math  /  Algebra

Question{c(1)=−20c(n)=c(n−1)+10\left\{\begin{array}{l} c(1)=-20 \\ c(n)=c(n-1)+10 \end{array}\right.
Find the 2nd 2^{\text {nd }} term in the sequence. □\square

Studdy Solution

STEP 1

1. We are given a recursive sequence defined by c(1)=−20 c(1) = -20 and c(n)=c(n−1)+10 c(n) = c(n-1) + 10 for n≥2 n \geq 2 .
2. We need to find the second term of the sequence, c(2) c(2) .

STEP 2

1. Identify the first term of the sequence.
2. Use the recursive formula to find the second term by substituting n=2 n = 2 .

STEP 3

Identify the first term of the sequence.
From the problem statement, we have: c(1)=−20 c(1) = -20

STEP 4

Use the recursive formula to find the second term by substituting n=2 n = 2 .
The recursive formula is: c(n)=c(n−1)+10 c(n) = c(n-1) + 10
Substitute n=2 n = 2 : c(2)=c(1)+10 c(2) = c(1) + 10

STEP 5

Substitute the value of c(1) c(1) into the equation.
We know c(1)=−20 c(1) = -20 , so: c(2)=−20+10 c(2) = -20 + 10

STEP 6

Simplify the equation to find c(2) c(2) .
c(2)=−20+10=−10 c(2) = -20 + 10 = -10
Solution: The second term in the sequence is c(2)=−10 c(2) = -10 .

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