Question

Find a1 when d= - 1 and a7= -2

Answer 1

`a_1=4`

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_7` = -2
• d = -1

Therefore:

`\implies a_7=-2`

`\implies a+(7-1)(-1)=-2`

`\implies a-6=-2`

`\implies a=4`

Therefore:

`\implies a_1=4`

Answer 2

• a₁ = 4

Explanation:

Given

• d = - 1
• a₇ = - 2

Find a₁

Use the nth term equation of AP

• aₙ = a₁ + (n - 1)d

Apply to the given case and solve for a₁

• - 2 = a₁ + 6(- 1)
• - 2 = a₁ - 6
• a₁ = 6 - 2
• a₁ = 4