Question

*The number of terms in the AP 2, 5, 8, …………., 59 is ………….*

1️⃣ c
2️⃣ 19
3️⃣ 20
4️⃣ 25​

Answer 1

Given :  AP 2, 5, 8, ______ 59  

To Find : number of terms in the AP

1️⃣ 14

2️⃣ 19

3️⃣ 20

4️⃣ 25​

Solution:

nth term of AP is given by

= a + (n - 1) d

a = 1st term

n = number of term

d = common difference

2, 5, 8, ______ 59  

a =  2

d = 3

last term = 59

59 = 2 + (n - 1) 3

=> 57 = (n - 1)3

=> 19 = n - 1

=> n = 20

number of terms in the AP  is 20

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Answer 2

Question :- The number of terms in the AP 2, 5, 8, …………., 59 is ………….

1) 17

2) 19

3) 20

4) 25

Solution :-

Let us assume that, the total terms in the AP is n .

we have given that,

First term of AP = a = 2

Common difference = d = second term - first term = 5 - 2 = 3

Last term = an = 59 .

total terms = n .

we know that,

an = a + (n - 1)d .

putting all values we get,

→ 59 = 2 + (n - 1)3

→ 59 = 2 + 3n - 3

→ 59 = 3n - 1

→ 59 + 1 = 3n

→ 3n = 60

→ n = 20 (Option 3) (Ans.)

Hence, The number of terms in the given AP is 20.

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