Question

4,11,22,49,141. ..............?
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Answer 1

Answer:

250.......................

Answer 2

Correct question is, 4,11,22,37,56. ..............?

Given:

4, 11, 22, 37, 56. ..............?

To find:

The next term of the series.

Solution:

From the given information, we have the data as follows.

4, 11, 22, 37, 56. ..............?

Let the given series be the sequence (the sum of series)

S_n = 4, 11, 22, 37, 56. ..............?  (1)

S_n =      4, 11, 22, 37, 56. ..............?  (2)

subtract the equations (1) and (2).

S = 4, 7, 11, 15, 19,.....

Therefore, the above sequence represents the A.P. series. So, we have,

S_n = n/2 [ 2a + (n - 1) d ]

Therefore, the nth term is given as follows.

a_n = 4 + (n - 1)/2 [14 + (n - 2) 4]

a_n = 4 + (n - 1) [7 + (n - 2) 2]

a_n = 4 + (n - 1) (2n + 3)

Substitute the numbers in the above equation.

a_1 = 4 + (1 - 1) (2 × 1 + 3) = 4

a_2 = 4 + (2 - 1) (2 × 2 + 3) = 11

a_3 = 4 + (3 - 1) (2 × 3 + 3) = 22

a_4 = 4 + (4 - 1) (2 × 4 + 3) = 37

a_5 = 4 + (5 - 1) (2 × 5 + 3) = 56

a_6 = 4 + (6 - 1) (2 × 6 + 3) = 79

Therefore, the next term of the series is, 79