Question

The first term of an arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the last term is 81.

Answer 1

53 terms

Explanation:

Finding common difference :

• a = 3
• a + 4d = 9
• 4d = 6
• d = 1.5

Solving :

• a_{n} = a + (n - 1)d
• 81 = 3 + 1.5n - 1.5
• 79.5 = 1.5n
• n = 53

Answer 2

n = 53

Explanation:

the sum to n terms of an arithmetic progression is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 3 and a₅ = 9 , then

3 + 4d = 9 ( subtract 3 from both sides )

4d = 6 ( divide both sides by 4 )

d = 1.5

then solving for n

3 + 1.5(n - 1) = 81 ( subtract 3 from both sides )

1.5(n - 1) = 78 ( divide both sides by 1.5 )

n - 1 = 52 ( add 1 to both sides )

n = 53

there are 53 terms in the progression