Grade 12th pass10 grade maths
7. Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.
7. Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.
1 Answer
Pawan Prajapati
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.
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