Question

The 10th term of AP is 52 and 16th term is 82. Find the 32nd term and the general term

Answer 1

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Answer 2

Given:

The 10th term of AP is 52 and the 16th term is 82.

To find:

The 32nd term and the general term of AP.

Solution:

The 32nd term of AP is 162 and the general term is 2 + 5n.

To answer this question, we should follow the following steps:

As we know in an A.P. having a = first term, d = common difference, the nth term is given by using the formula:

${n}^{th} \: term = a + (n - 1)d$

Now, as given,

The 10th term of AP = 52

So,

$a + (10 - 1)d = 52$

$a + 9d = 52 \: (i)$

and

The 16th term of AP = 82

$a + (16 - 1)d = 82$

$a + 15d = 82 \: (ii)$

On subtracting (i) from (ii), we get

$6d = 30$

$d = 5$

Now,

On putting the value of d in (i), we get

$a + 9(5) = 52$

$a = 52 - 45$

$a = 7$

Now,

The 32nd term of AP is

$= a + 31d$

$= 7 + 31(5)$

$= 7 + 155$

$= 162$

Now,

The general term of A.P. is given by:

$a + (n - 1)d$

$= 7 + (n - 1)5$

$= 7 + 5n - 5$

$= 2 + 5n$

Hence, the 32nd term of given A.P. is 162 and the general term is 2 + 5n.