Question

Middle term of given A.P. 2,7,12,.....52 is​

Answer 1

Given,

AP = 2,7,12, ----, 52

To find,

The middle term of the given AP.

Solution,

The middle term of the AP 2,7,12, ----, 52 will be 27.

We can easily solve this problem by following the given steps.

A.P. = 2,7,12, ----, 52

In this case, the first term (a) is 2, the common difference(d) is 5 (the second term - the first term), and the last term (an) is 52.

First, we have to find the number of terms (n) in the AP.

Using the formula to find the nth term,

an = a + (n-1)d

52 = 2 + (n-1)5

52 = 2 + 5n -5

52 = 5n-3

52+3 = 5n ( Moving 3 from the right-hand side to the left-hand side will result in the change of the sign from minus to plus.)

55 = 5n

n = 55/5

n = 11

So, there are a total of 11 terms in the AP which is an odd number.

Then, the middle term will be (n+1)/2.

Middle term = (11+1)/2

Middle term = 12/2

Middle term = 6

So, we have to find the sixth term.

Using the formula to find the nth term,

an = a + (n-1)d

a6 = 2 + (6-1)5

a6 = 2 + (5×5)

a6 = 2+25

a6 = 27

Hence, the middle term of the AP 2,7,12, ----, 52 is 27.