Q. 314.7( 29 Votes )

# Determine the nth term of the AP whose 7th term is - 1 and 16th term is 17.

Let a be the first term and d be the common difference.

Given: a7 = - 1

a16 = 17

Now, Consider a7 = - 1

a + (7 - 1)d = - 1

a + 6d = - 1 ……….(1)

Consider a16 = 17

a + (16 - 1)d = 17

a + 15d = 17 ……….(2)

Now, subtracting equation (1) from (2), we get,

9d = 18

d = 2

from equation (1), we get,

a = - 1 - 6d

a = - 1 - 6 × (2)

a = - 1 - 12

a = - 13

Now, the nth term of the AP is given by:

an = a + (n - 1)d

an = - 13 + (n - 1) × 2

an = 2n - 15

nth term of the AP is (2n - 15)

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