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Find the $n^{t h}$ term of the arithmetic sequence whose initial term and common difference term $d$ are given below respectively:
$a_{1} = 4, d = 3$
$a_{1} = - 8, d = 5$

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1 + 3 n, - 13 + 5 n

- 13 + 5 n, 1 + 3 n

1 - 3 n, 13 + 5 n

- 1 + 3 n, - 13 - 5 n

answer is A.

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Detailed Solution

Case A:→

a_{1} = 4, d = 3

n^{t h} term = a + (n - 1) d

(∵ formula of the

n^{t h}

term)

= 4 + (n - 1) 3

= 4 + 3 n - 3

= 1 + 3 n

— (|)
Case A:→

a_{1} = - 8, d = 5

Formula of the

n^{t h}

term,

n^{t h} term = a + (n - 1) d

= - 8 + (n - 1) 5

= - 8 + 5 n - 5

= - 13 + 5 n

— (||)
From (|) and (||), we can see that

n^{t h}

for

A

and

B

respectively is

1 + 3 n

and

- 13 + 5 n

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