Question

The rule to get from one term to the

next in a sequence is to multiply by 3
and then add x each time.
The first term in this sequence is 4.
The third term in this sequence is 56.
Work out the value of x.

Answer 1

x = 14

Explanation:

the formula for the arithmetic sequence is written as,

aₙ = a₁ + (n - 1)(d)

where

aₙ is the nth term of the arithmetic sequence

a₁ is the first term of the arithmetic sequence

n is the number of term of the arithmetic sequence

d is the difference in the terms of the arithmetic sequence

according to the given condition:

a₃ = 4 + (3 - 1)(3a₁ + x)

56 = 4 + (2)(3*4 + x)

56 = 4 + (2)(12 + x)

56 = 4 + 24 + 2x

56 - 28 = 2x

28 = 2x

x = 28/2 = 14

thus, the nth term would be defined as,

aₙ = a₁ + (n - 1)(3a₁ + 14)