Question

find the 31 trans of an ap whose 11th term is 38 and the 16 term is 73​

Answer 1

Step-by-step explanation:

Let a is first term and d is common difference in an A.P.

t11=a+(n-1)d

38=a+(11-1)d

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

t16=a+(n-1)d

73=a+(16-1)d

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

Subtracting equation(1) from (2)

38=a+10d

- 73=a+15d

- - -

-35= -5d

d= -35/-5

d= 7

Put d= 7 in equation (1)

38=a+10d

38=a+10×7

38=a+70

a=38-70

a= -32

t31=a+(n-1)d

t31= -32+(31-1)7

t31= -32+(30)7

t31= -32+210

t31= 178

Therefore,the 31 term is 178.