Find whether 55 is a term of the AP: 7, 10, 13,— or not. If yes, find which term it is

Solution:

Consider the first term, common difference and the number of terms of an AP are a, d and n.

nth term of an AP is Tn = 55

We know that the nth term of an AP,

T_n= a + (n - 1 )d …………….. (i)

It is given,

first term (a) = 7

common difference (d) = 10 - 7 = 3

From equation (i),

55 = 7 + (n - 1) × 3

55 = 7 + 3n - 3

55 = 4 + 3n

3n = 51

Dividing both sides by 3

n = 17

n is a positive integer. So 55 is a term of the AP as n = 17

Therefore, the 17th term of an AP is 55.

✦ Try This: Find whether 44 is a term of the AP: 8, 11, 14,— or not. If yes, find which term it is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 10

Find whether 55 is a term of the AP: 7, 10, 13,— or not. If yes, find which term it is

Summary:

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. 55 is a term of the AP: 7, 10, 13,—. It is the 17th term

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