Question

Find the number of terms and the expression for the nth term of the following Aps 1, 8, 15,....,78

Answer 1

see explanation

Explanation:

the nth term of an arithmetic progression is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 , d = a₂ - a₁ = 8 - 1 = 7 and
`a_(n)` = 78 , then

1 + 7(n - 1) = 78 ( subtract 1 from both sides )

7(n - 1) = 77 ( divide both sides by 7 )

n - 1 = 11 ( add 1 to both sides )

n = 12

that is there are 12 terms in the progression.

from above

`a_(n)` = 1 + 7(n - 1) = 1 + 7n - 7 = 7n - 6

then nth term is

`a_(n)` = 7n - 6