1.

Find 20th term of an AP whose 5th term is 13 and 9th term is 21​

Answer»

GIVEN

find 20th term of an AP whose 5th term is 13 and 9th term is 21

SOLUTION

  • a5 = 13
  • a9 = 21

→ an = a + (N - 1)d

→ a5 = a + (5 - 1)d

→ 13 = a + 4d

→ a + 4d = 13 ------(i)

Now,

→ a9 = a + (n - 1)d

→ 21 = a + (9 - 1)d

→ 21 = a + 8d

→ a + 8d = 21 ------(ii)

Subtract both the equations

→ (a + 4d) - (a + 8d) = 13 -21

→ a + 4d - a - 8d = 8

→ -4d = - 8

→ d = 8/4 = 2

Putting the value of d in equation (i)

→ a + 4d = 13

→ a + 4*2 = 13

→ a + 8 = 13

→ a = 13 - 8 = 5

First term = 5

Common difference = 2

→ a20 = a + (n - 1)d

→ a20 = 5 + (20 - 1)2

→ a20 = 5 + 19*2

→ a20 = 5 + 38

→ a20 = 43

Hence, 20th term of A.P is 43


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