Question

how many terms are there in ap 7,11,15,......,139?

Answer 1

AP : 7 , 11 , 15 ,... 139

a = 7 , d = 11 - 7 = 4 , n = ?

Last term = 139

Tn = 139

a + (n - 1)d = 139

7 + (n - 1)4 = 139

(n - 1)4 = 139 - 7

(n - 1) = 132/4

n - 1 = 33

n = 33 + 1

n = 34

Hence,

There are 34 terms in Given AP.

Answer 2

Given:

An A.P series 7, 11, 15, .., 139.

To Find:

The number of terms in the above A.P is?

Solution:

The given problem can be solved using the concepts of arithmetic progressions.

1. The given series is 7, 11, 15, .., 139.

2. Consider an A.P with the first term 'a', Common Difference 'd', and the number of terms as 'n'. The formula for the nth term of an A.P is given by the formula,

=> Tn = a + ( n - 1 )d,

=> Common difference = t2 - t1 = t3 - t2 = t4 - t3 = .. = tn - tn-1,

=> Common difference = 11 - 7 = 4,

=> Here a = 7, d = 4, Tn = 139.

=> 139 = 7 + ( n - 1 )4,

=> 139 - 7 = 4n - 4,

=> 132 + 4 = 4n,

=> n = (136)/4,

=> n = 34.

Therefore, the number of terms in the given A.P is 34.