Find the 31^{st} term of an A.P. whose 11^{th} term is 38 and the 16^{th} term is 73

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#### Solution

Given that,

a_{11} = 38

a_{16} = 73

We know that,

a_{n} = a + (n − 1) d

a_{11} = a + (11 − 1) d

38 = a + 10d (1)

Similarly,

a_{16} = a + (16 − 1) d

73 = a + 15d (2)

On subtracting (1) from (2), we obtain

35 = 5d

d = 7

From equation (1),

38 = a + 10 × (7)

38 − 70 = a

a = −32

a_{31} = a + (31 − 1) d

= − 32 + 30 (7)

= − 32 + 210

= 178

Hence, 31^{st} term is 178.

Concept: nth Term of an AP

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