Question

Which term of the A.P. 3, 10, 17, … will be 84 more than its 13th term ?

25

27

28

30

​

Answer 1

Answer:

Here,

a = 3

d = 7

an = a13 + 84

⇒a+(n−1)d=(a+12d)+84

⇒(n−1)d=12d+84

⇒(n−1)7=12×7+84

⇒(n−1)7=7(12+12)

⇒n−1=24

⇒n=25

Answer 2

Answer :

25th term will be 84 more than its 13th term . [Option 1]

Step-by-step explanation :

Given :

• First term (a) = 3

• Common difference (d) = 7

To find :

• Which term of the A.P. 3, 10, 17, … will be 84 more than its 13th term = ?

SoluTion :

According to the question, 13 term will be,

➟a13 = a + 12d

➟a13 = 3 + 12×7

➟a13 = 3+ 84

➟a13 = 87

Also, it is given that the term will be 84 more than its 13th term = 87 + 84 = 171 .

Now,

➝ an = a+(n-1)d

➝ 171 = 3 + 7n - 7

➝ 171 + 4 = 7n

➝ 175/7 = n

➝ n = 25

Hence, 25th term will be 84 more than its 13th term .

VeriFication :

It is given that the term will be 84 more than its 13th term ,

⇛ a25 = a + 24d

⇛ a25 = 3 + 24×7

⇛ a25 = 3 + 168

⇛ a25 = 171

Some important formulae :

1. General form of an Arithmetic Progression is

• a, a + d, a + 2d, a + 3d and so on

2. Sum of first n terms of an AP is given as,

• S =(n/2)[2a + (n- 1)d]

3. Sum of n terms is given by,

• Sn = n/2 × (a + l)

4. If a, b & c are 3 terms in AP then,

• b = (a+c)/2