Question

 what is the nth term for 6, 10, 4, 12, 2, 14, 0, 16, −2, . . ​

Answer 1

6=1+2+3

10=1+2+3+4

4=1+3

12=1+2+3+4+2

2=1+2

14=1+2+3+4+2+2

0=is not defined

16=1+2+3+4+2+2+2

-2=not in defined

Answer 2

Concept

In mathematics, a series is a description of the operation of adding infinitely many quantities, one after the other, starting from a given quantity.

Given

a series 6, 10, 4, 12, 2, 14, 0, 16, −2, . . ​

Find

We have to find the nth term of the series

Solution

We have,

6, 10, 4, 12, 2, 14, 0, 16, −2, . . ​

The odd terms of the series are-

a1 = 6 (7 -1)

a3 = 4 (7 -3)

a5 = 2 (7- 5)

a7 = 0 (7 -7)

a9 = -2 (7 -9)

Here, we see a pattern,

the nth term will be (n-7)

The even terms of the series are-

a2 = 10 (8 +2)

a4 = 12 (8 +4)

a6 = 14 (8 +6)

a8 = 16 (8 +8)

Here, we see a pattern,

the nth term will be (8 + n)

Thus the nth term will be,

(n-7), if n is odd

(8+n), if n is even

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