Question

99th term of the series: 2+7+14+23+34+......

Answer 1

Answer:

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The first level of differences are 5,7,9,11 and so on

The second level of differences is 2,2,2,2… [there can’t be a third level of differences as all the second level of differences are the same]

Now, given that there are two levels of differences,

U - term

n - term no. [variable]

a,b,c - constants

U[n] = a n2 + bn +c

In a sequence with two levels of differences, you can equate the first number in each level with certain expressions.

If 2a = 2, then a = 1.

Now, the expression for the first number of the first level of difference, 5, the expression will be 3a+b. So,

3a+b = 5

3(1) + b = 5

Therefore, b = 2

Now, to find c, you’ll use the first term of the sequence itself. So for 2, the expression will be a+b+c [for cubic it’s a+b+c+d and so on]. So,

a + b + c = 2

(1) + (2) + c = 2

Therefore, c = -1.

So the equation will be U[n] = n2 + 2n - 1

Input n as “99” to find the 99th term:

U[99] = 992 + 2 (99) -1

= 9801 + 198 - 1

= 9998

Thus, the 99th term of the sequence will be 9998 .

Hope it will be helpful :)

Answer 2

Answer:

Refers to the attachment