Question

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

Answer 1

Answer:

hellø

Step-by-step explanation:

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 ... (i)

Similarly,

a

16

=a+(16−1)d

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

On subtracting (i) from (ii), we get

35=5d

∴d=7

From equation (i),

38=a+(10)(7)

⇒38−70=a

∴a=−32

Now a

31

=a+(31−1)d

=−32+30(7)

=−32+210

=178

Hence, 31

st

term is 178

Answer 2

Given, a11 = 38 and a16 = 73

We know that an = a + (n – 1)d

Hence, a11 = a + 10d = 38

And, a16 = a + 15d = 73

Subtracting 11th term from 16th term, we get following:

a + 15d – a – 10d = 73 – 38

Or, 5d = 35 Or, d = 7

Substituting the value of d in 11th term we get;

a + 10 x 7

= 38 Or, a + 70 = 38

Or, a = 38 – 70 = - 32

Now 31st term can be calculated as follows:

a31 = a + 30d

= - 32 + 30 x 7

= - 32 + 210 = 178