Question

In an arithmetic sequence if a1 =7 and d = 3, find a64

Answer 1

196

Explanation:

Formula for the nth term

• aₙ = a₁ + (n - 1) d

Taking n = 64

• a₆₄ = 7 + 63(3)
• a₆₄ = 7 + 189
• a₆₄ = 196

Answer 2

`a_(64)=196`

Explanation:

Arithmetic sequence

General form of an arithmetic sequence:
`a_n=a+(n-1)d`

where:

• 
  `a_n` is the nth term
• a is the first term
• d is the common difference between terms

Given:

• 
  `a_1=7`

• 
  `d=3`

Substituting these into the equation to find the nth term:

`\implies a_n=7+(n-1)3`

`\implies a_n=3n+4`

To find the 64th term, substitute n = 64 into the formula:

`\implies a_(64)=3(64)+4=196`