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Home » Choose the correct answer from the given four options in the following questions: If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term? (A) 30 (B) 33 (C) 37 (D) 38
Choose the correct answer from the given four options in the following questions: If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(A) 30 (B) 33 (C) 37 (D) 38
Arithmetic Progression | CBSE | Class 10 | Exercise 5.1 | Maths | NCERT Exemplar
Choose the correct answer from the given four options in the following questions: If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(A) 30 (B) 33 (C) 37 (D) 38

Solution:

Option (B) 33 is the correct option.

Explanation:

It is known that the AP’s nth term is

{{a}_{n\text{ }}}=~a\text{ }+\text{ }\left( n-1 \right)d

In which,

first term = a

nth term = an

common difference = d

{{a}_{2\text{ }}}=~a\text{ }+\text{ }d\text{ }=\text{ }13…..(1)

{{a}_{5\text{ }}}=~a\text{ }+\text{ }4d\text{ }=\text{ }25…… (2)

From eq. (1) we have,

a=13-d

Using this in eq. (2), we have

13-d+4d=25

13+3d=25

3d=12

d=4

a=13-4=9

{{a}_{7\text{ }}}=~a\text{ }+\text{ }6d

=9+\text{ }6\left( 4 \right)

=\text{ }9\text{ }+\text{ }24\text{ }=\text{ }33

i

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