Question

Can someone pls help

Answer 1

Answer: common difference is 3, 21st term is 65.

Explanation:

The mistake is in the common difference. They divided by 3, which is the number of missing terms in the middle, but you need to always divide by one more than the missing term because you need to get to the filled ter, at the end. You have to do 17-5=12, 12/4=3 so the common difference is 3.

Now use the formula to get 5+3(21-1)=65

Answer 2

d = 3 , a₂₁ = 65

Explanation:

the error has been made in subtracting the first term from the fifth term.

the common difference d is the difference between consecutive terms.

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

a₁ is the first term , d the common difference

given a₅ = 17 , then

a₁ + 4d = 17

substitute a₁ = 5

5 + 4d = 17 ( subtract 5 from both sides )

4d = 12 ( divide both sides by 4 )

d = 3

Then

a₂₁ = a₁ + 20d = 5 + 20(3) = 5 + 60 = 65