Answer:
n = 99
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 1 , d = 2 and [tex]S_{n}[/tex] = 9801 , then
[tex]\frac{n}{2}[/tex] [ (2 × 1) + 2(n - 1) ] = 9801 ( multiply both sides by 2 to clear the fraction )
n(2 + 2n - 2) = 19602
n(2n) = 19602
2n² = 19602 ( divide both sides by 2 )
n² = 9801 ( take the square root of both sides )
n = [tex]\sqrt{9801}[/tex] = 99
The number of terms summed is 99
