Question

determine the nth term of the AP whose 7th term is - 1 and 16th term is17

Answer 1

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Let , a be the first term and d be the common difference of the A.P .

Than ,


T17 = -1

=> a + (n-1 ) d = -1
=> a + 6d = -1 ....... ( ¡ )

Also

T16 = a + ( 16 - 1 ) d = -1

=> a + 15d = -1 ....... ( ¡¡ )

From 1 and 2 , we get

$- 1 - 6d + 15d = 17 \\ \\ = > 9d = 17 + 1 = 18 \\ \\ d = \frac{18}{9} = 2 \\ \\ d = 2 \\ \\ putting \: \: d = 2 \: \: in \: 1 \: \: we \: get \: \\ \\ a + 6 \times 2 = - 1 \\ a = - 1 - 12 = - 13$


● Tn = a + ( n - 1 ) d

=> - 13 + ( n -1 )2

=> -13 + 2n - 2

=> -13 - 2

=> 2n - 15

Hence , the nth term of the A.P is ( 2n - 15 ).

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