Question

How many terms are there in the arithmetic series 5,7,9..75​

Answer 1

Hint: Recall the formula of nth term of AP to find the value of n (which is the number of terms of AP).

Solution :-

By the given information in the question, we have:-

• The AP is 5, 7, 9, . . . , 75
• First term of AP = 5
• Common difference of AP = 2

[Common difference of AP can be obtained by substracting any term from it's previous term].

We have the equation of general form of any term of the AP as mentioned below:

• $\sf a_n = a - (n - 1)d$

Here,

• $\sf a_n = nth\,term \,of\,AP$
• $\sf a= First\,term \,of\,AP$
• $\sf d = Common\, difference \,of\,AP$
• $\sf n = number\,of\,terms \,of\,AP$

By substituting the known values of a, d and an in the general equation, we get:

$\sf\implies a_n = a + (n - 1)d$

$\sf\implies 75 = 5 + (n - 1)(2)$

$\sf\implies 75 - 5 = (n - 1)(2)$

$\sf\implies 70= (n - 1)(2)$

$\sf\implies \dfrac{70}{2} = (n - 1)$

$\sf\implies 35 = (n - 1)$

$\sf\implies 35 + 1= n$

$\boxed{ \tt\implies 36= n }$

Hence, 75 is the 36th term of AP.

Required answer is 36