Question

Find 21st tern of an Ap whose last 11 term is 38 and 16 term is 73

Answer 1

We know that

a, = a + (n - 1) d

Given 11th term is 38

a11 = a + (11-1) d

38 = a + (11-1)d

38 = a + 10 d

38-10 d = a

a = 38 - 10d.........(1)

Given 16th term is 73

а16= а + (16-1)d

a16 = a + 15d

73 = a + 15d

73 - 15d = a

a = 73-15d.......(2)

From (1) & (2)

38 - 10d = 73- 15d

38 - 73 = - 15d - 10d

- 35 = -5d

d= -35/-5

d = 7

Putting the value of d in (1)

a = 38-10 d

a = 38-10x 7

a = 38-70

a = - 32.

We need to find the 31st term

So, n = 31, a = -32, d = 7

an = a + (n - 1) d

Putting values

a31 = -32 + (31- 1) 7

= - 32 + 30 X 7

=-32 + 210

= 178

Therefore, the 31st term of AP is 178

HOPE THIS HELPS YOU.

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