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Arithmetic Progressions
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31/05/2021 11:26 am
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Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.
1 Answer
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31/05/2021 11:28 am
Given that,
11th term, a11 = 38
and 16th term, a16 = 73
We know that,
an = a+(n - 1)d
a11 = a+(11 - 1)d
38 = a+10d …………………. (i)
In the same way,
a16 = a +(16−1)d
73 = a+15d ………………… (ii)
On subtracting equation (i) from (ii), we get
35 = 5d
d = 7
From equation (i), we can write,
38 = a+10×(7)
38 - 70 = a
a = -32
a31 = a +(31 - 1) d
= - 32 + 30 (7)
= - 32 + 210
= 178
Hence, 31st term is 178.