find the 31st term of an ap whose 11th term is 38 and the 16th term is 73
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T11=38
a+(n-1)d..............where n=11
a+10d=38
a=38-10d........eq(i)
T16=73
a+15d=73
putting the value of a from eq(i)
38-10d+15d=73
5d=73-38
5d=35
d=7
putting the value of d in eq (i)
a=38-10d
=38-10×7
=38-70
=-32
Hence ,T31=a+30d=-32+30×7=-32+210=178
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11th term of AP is 38 and,
16th term of AP is 73.
The 31st term of AP = ?
Let first term of AP be a
Let first term of AP be aand common difference be d
Let first term of AP be aand common difference be dNow,
And,
From eq (i) and eq (ii),
a + 10d = 38 ‿︵‿︵│
⠀ ⠀ ⠀ ⠀⠀⠀ ⠀ ⠀ ⠀⠀⠀ ⠀ |Subtracting
a 15d = 73 ‿︵‿︵│
-⠀ -⠀ ⠀ -
━━━━━━━━━━━━━━
-5d = -35
Now,
Substitute the value of d in equation (i),
Then,
Hence, the 31st term of an AP was
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