Pattern Practice, College Mathematics

Question

X, 2X + 11 and 4X - 3 are consecutive terms of an arithmetic sequence.

1. Find the constant difference between terms.
2. Give a formula for finding the nth term of the sequence.
3. Use your formula to find the 27th term of this sequence.

Answer 1

Hello Hannah.

If we have an algebraic sequence then there is a constant difference;

(4x -3) - (2x+11) = (2x +11) - x

2x - 14 = x +11

x = 25

our sequence is 25, 61, 97 ...

1. constant difference is 61-25 = 36.
2.  a_n = a₁ + (n-1) d is general formula where a_n is nth term and d is difference
3. a₂₇ = a₁ + (27-1)*36 = 25+ 26*36 = 961

hope that helps