Question

Find the middle term of the A.P. 3, 8, 13,......, 253 *

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

A.P. = 3,8,13, ---, 253

To find,

The middle term of the given A.P.

Solution,

The middle term of the A.P. 3,8,13, ---, 253 will be 128.

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

According to the question,

3,8,13, ---, 253

The first term (a) of the A.P. is 3 and the last term (an) is 253 where n is the number of total terms of the series.

The common difference(d) can be found by subtracting the first term from the second term.

d = a2 - a1

d = 8-3

d = 5

Now, using the formula to find the last term, we have

an = a + (n-1)d

253 = 3 + (n-1)5

253 = 3+5n-5

253 = 5n-2

5n-2 = 253

5n = 253+2 ( Moving 2 from the left-hand side to the right-hand side results in changing the sign from minus to plus.)

5n = 255

n = 255/5

n = 51

So, there are a total of 51 terms in the given series.

Because it is an odd number the middle term will be found using the formula, (n+1)/2.

Middle term = (n+1)/2

Middle term = (51+1)/2

Middle term = 52/2

Middle term = 26

Then, the 26th will be a26.

an = a+(n-1)d

a26 = 3 + (26-1)5

a26 = 3+ (25)5

a26 = 3+125

a26 = 128

Hence, the middle term of the given A.P. is 128.