Question

If I start with the number 7 and count by 4s, the following sequence is obtained: 7, 11, 15, 19, 23, and so forth. A new sequence is formed when I start with a different number and count by a different number. Suppose the 2nd number of the new sequence is 8 and the 5th number is 17. What is the 10th number of the new sequence

Answer 1

a₁₀ = 32

Explanation:

the sequence is arithmetic since there is a count on , a common difference

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₂ = 8 and a₅ = 17 , then

a₁ + d = 8 → (1)

a₁ + 4d = 17 → (2)

subtract (1) from (2) term by term to eliminate a₁

3d = 9 ( divide both sides by 3 )

d = 3

substitute d = 3 into (1)

a₁ + 3 = 8 ( subtract 3 from both sides )

a₁ = 5

Then

a₁₀ = 5 + (9 × 3) = 5 + 27 = 32