Find the 31 term of an ap whose 11th term is 38 and the 16th term is 73
Answers
Given:
11th term is 38 and the 16th term is 73.
Find:
The 31th term of an AP
Solution:
The 11th term of Ap is 38
The 16th term of Ap is 73
we know that;
The 11th term of Ap is 38
=> an = a + (n - 1)d
=> a11 = a + (11 - 1)d
=> 38 = a + 10d .............(i).
The 16th term of Ap is 73
=> an = a + (n - 1)d
=> a16 = a + (16 - 1)d
=> 73 = a + 15d .............(ii).
Now, Subtracting Eq. (ii) and (i) we get,
=> d = 35/5
=> d = 7
Now, putting the value of d in Eq. (i).
=> a + 10d = 38
=> a + 10(7) = 38
=> a + 70 = 38
=> a = 38 - 70
=> a = - 32
So,
=> a31 = a + (31 - 1)d
=> a31 = a + 30d
=> a31 = - 32 + 30 × 7
=> a31 = - 32 + 210
=> a31 = 178
Hence the 31th term of Ap is 178.
I hope it will help you.
Regards.
Answer:
Given that, a11 =38 a16 =73
We know that,
a^n=a+(n−1)d
a11 =a+(11−1)d
38=a+10d ... (i)
Similarly,
a16 =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 a31 =a+(31−1)d
=−32+30(7)
=−32+210
=178
Hence, 31^st term is 178.
Hope this is helpful for you.