Question

Please help someone. {1,4,9,16...}
what are the next three members?

Answer 1

The solution is 25, 36, 49

Explanation:

a = 1

b = 3

c = 5-3

= 2

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Un =
`\sf a + (n-1) * b + ((n-1)(n-2))/(2) * c`

Un =
`\sf 1 + (n-1) * 3 + ((n-1)(n-2))/(2) * 2`

Un =
`\sf 1 + 3n-3 + (n-1)(n-2)`

Un =
`\sf 1 + 3n-3 + n^(2) - 2n - n + 2`

Un =
`\sf n^(2) + 3n - 2n - n + 2 + 1 - 3`

Un =
`\sf n^(2) + 0n + 0`

Un =
`\sf n^2`

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Un = n²

U5 = 5²

= 25

U6 = 6²

= 36

U7 = 7²

= 49

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So, the next three members are 25, 36, 49