Question

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

Answer 1

Answer:

178 is the 31st term of AP

Step-by-step explanation:

Given : a11 = 38

a16 = 73

=> an = a + (n-1) d

=> a11 = a + (11-1) d

=> a + 10d = 38 ———— eq 1

=> a16 = a + (16-1) d

=> a + 15d = 73 ———— eq 2

Now subtract eq 1 - 2

It becomes : -5d = -35

=> d = -35/-5

=> d = 7

Now insert the value of d in eq 1

=> a + 70 = 38

=> a = -32

Now 31st term of AP is : n =31

=> an = -32 + (31 - 1) 7

=> a31 = -32 + 210

=> a31 = 178 Answer

Hope this will help you friend

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Answer 2

EXPLANATION.

=> 11 th term of an Ap = 38

=> 16 th term of an Ap = 73

To find the 31st term of an Ap.

Formula of Nth term of an Ap

=> An = a + ( n - 1 ) d

=> 11th term = 38

=> a + 10d = 38 .......(1)

=> 16th term = 73

=> a + 15d = 73 .......(2)

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

=> - 5d = - 35

=> d = 7

put the Value of d = 7 in equation (1)

we get,

=> a + 10(7) = 38

=> a + 70 = 38

=> a = -32

Therefore,

31 st term of an Ap

=> a + 30d

=> -32 + 30(7)

=> -32 + 210

=> 178

31 st term of an Ap = 178.