Question

Find the 105th term of the
a.p 4,4 1/2,5,5 1/2,6......

Answer 1

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Answer 2

Given:

An A.P.

$4, \: 4 \frac{1}{2}, \: 5, \: 5 \frac{1}{2}, \: 6...$

To find:

The 105th term of the A.P.

Solution:

To answer this question, first of all, we should know that the nth term of an A.P. is given by using the formula

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

where a = first term, d = common difference between two consecutive terms.

Now,

as given, we have an A.P.

$4, \: 4 \frac{1}{2}, \: 5, \: 5 \frac{1}{2}, \: 6...$

here a = 4

the common difference, d = 1/2

$(d = 4 \frac{1}{2} - 4)$

and

n = 105

So,

105th term

$= 4 + (105 - 1) \frac{1}{2}$

$= 4 + 104( \frac{1}{2})$

$= 4 + 52$

$= 56$

Hence, the 105th term of the given A.P. is 56.