Question

Complete the series : 1,8, 22, 43, 71, solve this problem​

Answer 1

Answer:

A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for n is given by the formula

{\displaystyle {7n^{2}-7n+2} \over 2} {7n^2 - 7n + 2}\over2.

This can also be calculated by multiplying the triangular number for (n – 1) by 7, then adding 1.

The first few centered heptagonal numbers are

1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953 (sequence A069099 in the OEIS)

Centered heptagonal numbers alternate parity in the pattern odd-even-even-odd.

Answer 2

1 , 8 , 22 , 43 , 71 , 106

Solution:

Given series:

1 , 8 , 22 , 43 , 71 ,

We have to find the next term in series

Let us analyse the logic used in series

$First\ term = 1\\\\Second\ term = 1 + 7 = 8\\\\Third\ term = 8 + 14 = 22\\\\Fourth\ term = 22 + 21 = 43\\\\Fifth\ term = 43 + 28 = 71$

Thus, successive term are found by adding multiples of 7 with previous term

Therefore,

$Next\ term = 71 + 35 = 106$

Thus the next term in series is 106

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