Question

The 13th term of an ap is 4 times third term if its 5th term is 16 then find the first term and common difference

Answer 1

Answer:

Step-by-step explanation:

An=a+(n-1)d

a13=4(a+2d)

a+12d=4a+8d

3a-4d=0...........................1

a5=16

a+4d=16..............................2

From eq 1,2

3a-4d=0

a+4d=16

4a=16

a=16/4

a=4..................3putting it in eq2

4+4d=16

d=16-12/4

d=3

Answer 2

➾ Answer :

→ First term = 4

→ common Difference = 3

➾ Step - By - Step Explanation :

➾ Given :

→ The 13th term of an AP is 4 times third term if its 5th term is 16

→ T13 = 4 (T3) ------(A)

→ T5 = 16 --------(B)

➾ Solution :-

From Equation ( A ) :

→ T13 = 4 (T3)

⇒ a + 12d = 4 ( a + 2d )

⇒ a + 12d = 4a + 8d

⇒ 4a - a + 8d - 12d = 0

⇒ 3a - 4d = 0. ------(I)

Now, From Equation ( B)

→ T5 = 16

⇒ a + 4d = 16. -------(II)

Solving Equations ( A) and (B) :

3a - 4d = 0.

a + 4d = 16
___________
4a = 16
____________

⇒ a = 4

Now, Putting Value of a in Equation (1)

→ 3a - 4d = 0

→ 3 (4 ) - 4d = 0

→ 12 - 4d = 0

→ 4d = 12

→ d = 3

Hence, Required Value of First term (a) and It's common Difference (d) of the Arithmetic Progression are 4 and 3 respectively.