7. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Answers
ANSWER:
- 31st term of given A.P is 178
GIVEN:
- 11th term of an A.P is 38.
- 16th term of an A.P is 73.
TO FIND:
- 31st term of the A.P.
SOLUTION:
Formula:
=> nth term = a+(n-1)d
Let the first term of the A.P be 'a' and the common difference be 'd'.
=> 11th term = 38
=> a+(11-1)d = 38
=> a+10d = 38 .....(i)
=> 16th term = 73
=> a+(16-1)d = 73
=> a+15d = 73 ....(ii)
Subtracting eq (I) from (ii)
=> a+15d-a-10d = 73-38
=> 5d = 35
=> d = 35/5
=> d = 7
Putting d = 7 in eq(I) we get.
=> a+10(7) = 38
=> a+70 = 38
=> a = 38-70
=> a = (-32)
here :
=> a = (-32)
=> d = 7
=> 31st term = a+(31-1)d
=> 31st term = (-32)+30(7)
=> 31st term = 210-32
=> 31st term =178
So 31st term of given A.P is 178
GIVEN:
11th term of an AP = 38
16th term of an AP = 73
TO FIND:
31st term of AP
SOLUTION:
11th term = a + 10d = 38 ----(1)
16th term = a + 15d = 73 ----(2)
Solve both eq - (1) & (2)
==> -5d = -35
==> d = 35/5
==> d = 7
Common Difference = 7
Substitute (d) in eq - (1) to find first term (a)
==> a + 10(7) = 38
==> a + 70 = 38
==> a = 38 - 70
==> a = -32
First term = -32
Now, let's find the 31st term of AP
31st term = a + 30d
= -32 + 30(7)
= -32 + 210
= 178
Therefore, the 31st term of AP is 178.