Question

find the nth term of a fractional sequences
$1 \frac{6}{5} \frac{7}{5} \frac{8}{5} \frac{9}{5} 2$
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Answer 1

The nth term of the factorial sequences is $a_n$ = 9/5 + (1/5)n

Given: First term, $a_1$ = 1, second term, $a_2$ = 6/5 and third term, $a_3$ = 7/5

Common difference in terms, d = a₂ - a₁ = $\frac{6}{5} - 1$ = $\frac{1}{5}$

and $a_3 - a_2$ = 1/5

The common difference between the terms is same. Hence, the given factorial sequence is an Arithmetic Progression.

This is an arithmetic progression with common difference, d = 1/5.

nth term formula for an A.P is $a_n$ =  a + (n-1)d

where,

n = no of terms

By using the formula of nth term:

$a_n$ = 2 + (1/5)×(n-1)

$a_n$ = 2 - 1/5 + (1/5)n

⇒ $a_n$ = 9/5 + (1/5)n

The nth term of the given fractional sequences is $a_n$ = 9/5 + (1/5)n

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