# The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.

Let a and d be the first term and common difference of the AP Given: a17 = 2 × a8 + 5

a11 = 43

To find: nth term = an

Consider a11 = 43

a + (11 - 1)d = 43

a + 10d = 43 ………….. (1)

Consider a17 = 2 × a8 + 5

a + (17 - 1)d = 2[a + (8 - 1)d] + 5

a + 16d = 2a + 14d + 5

- a + 2d = 5 ……………….(2)

Adding equation (1) and equation (2), we get

12d = 48

d = 4

from equation (1), we get,

a = 43 - 10d

= 43 - 40

= 3

Now, nth term is given by:

an = a + (n - 1)d

an = 3 + (n - 1)4

an = 4n - 1

Therefore, nth term is given by (4n - 1).

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