Question

Find the second term and nth term of an A.P. whose 6th term is 12 and 8th term is 22.

Answer 1

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Answer 2

Given :

Sixth term of an A.P = 12

a + 5d = 12 ------(1)

Eighth term of an A.P = 22

a + 7d = 22 ----(2)

Solve eq - (1) & (2) to find difference (d)

a + 5d = 12

a + 7d = 22

(-)

-----------------

-2d = -10

d = 10/2

d = 5

Difference = 5

Substitute d in eq - (1) to find first term (a)

a + 5d = 12

a + 5(5) = 12

a + 25 = 12

a = 12 - 25

a = -13

First term = -13

Second term :

= a + d

= -13 + 5

= -8

an = a + ( n - 1 )d

= -13 + ( n - 1) 5

= -13 + 5n - 5

= -18 + 5n

= 5n - 18

Therefore, nth term of A.P is 5n - 18 and second term of A.P is -8.