Question

The sum of N terms of an arithmetic sequence with first term as 1 and common difference of 2 is 9801. Calculate the value of N.

Answer 1

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Answer 2

n = 99

Explanation:

The sum to n terms of an arithmetic sequence is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 1 , d = 2 and
`S_(n)` = 9801 , then

`(n)/(2)` [ (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 =
`√(9801)` = 99

The number of terms summed is 99