Question

What is the nth term of the series 5,6,8,12,20,36,...​

Answer 1

a = 5

d = 1

an=a+(n-1)d

an=5+(n-1)1

an=5+(1n-1)

1n=4

n=4

Answer 2

Answer:

Nth term for series = a + nth term - 1 = (a-1) + 2ⁿ-¹ = {4 + 2ⁿ-¹}

Step-by-step explanation:

Given series is 5 , 6 , 8 , 12 , 20 , 36 , ......n term

finding the difference between preceding and next term

we get a new series 1 , 2 , 4 , 8 , 16 , 32 , 64......

6 - 5 = 1

8 - 6 = 2

12 - 8 = 4

20 - 12 = 8

36 - 20 = 16

hence, new series is in the form of gp

so, nth term of gp is , nth = (1)(2)ⁿ-¹ = 2ⁿ-¹

where, a = 1 , common ratio r = 2

now, for N th term of previous series

Nth term = a + nth term - 1 = (a-1) + 2ⁿ-¹ = {4 + 2ⁿ-¹}

for example, 3term

3rd term = 5 + 2³-¹ - 1

3rd term = 5 + 2² - 1

3rd term = 5 + 4 - 1 = 8

for 5th term N = 5 , n = 5

5th term = 4 + 2⁵-¹

5th term = 4 + 2⁴

5th term = 4 + 16 = 20

5th term = 20

hence, verified

Thanks,

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