The recursive equation of a sequence is given by a Subscript n Baseline equals a Subscript n minus 1 Baseline plus 7 for n is greater than or equal to 1.

Question

If a Subscript 5 Baseline equals 43, what is a Subscript 1 Baseline?

Answer options with 5 options
A.
1

B.
6

C.
8

D.
10

E.
15

Answer 1

To solve for \( a_1 \) given the recursive equation \( a_n = a_{n-1} + 7 \) for \( n \geq 1 \) and the condition \( a_5 = 43 \), we can work backwards through the sequence.

1. Starting from \( a_5 \): \[ a_5 = a_4 + 7 \] Since \( a_5 = 43 \): \[ 43 = a_4 + 7 \implies a_4 = 43 - 7 = 36 \]

2. Now calculate \( a_4 \): \[ a_4 = a_3 + 7 \] From above, \( a_4 = 36 \): \[ 36 = a_3 + 7 \implies a_3 = 36 - 7 = 29 \]

3. Calculate \( a_3 \): \[ a_3 = a_2 + 7 \] From above, \( a_3 = 29 \): \[ 29 = a_2 + 7 \implies a_2 = 29 - 7 = 22 \]

4. Calculate \( a_2 \): \[ a_2 = a_1 + 7 \] From above, \( a_2 = 22 \): \[ 22 = a_1 + 7 \implies a_1 = 22 - 7 = 15 \]

Thus, we find that \( a_1 = 15 \).

The answer is \( \boxed{15} \).