Question

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

Answer 1

Ans-a=-32 and d=7

a31-188

Answer 2

Answer:

178 is the 31st term if this AP

Step-by-step explanation:

a11=a+(n-1)d

a11=a+(11-1)d

38=a+10d this is eq. 1

a16=a+(n-1)d

73=a+(16-1)d

73=a+15d this is eq. 2

subtract these equations,eq. 2 - eq. 1

we get 35=5d

d=35/5=7

now, substitute d in eq. 1

38=a+10d

38=a+10 x 7

a= - 42

as we got both a = - 42 and d = 7 we can find a31

a31=a+(n-1)d

a31= - 32+(31 - 1)7

a31=178

Hence the problem is solved and 31 st term od AP is 178