Determine A.P whose 3rd term is 5 and the 7th term os 9
Answers
Required solution :
Here, we've been provided with the 3rd and 7th term of an A.P. and required to calculate the A.P. !
So simply we would be using the formula of calculating the nth term or general term of an A.P. !
★ General or nth term of A.P. :-
- tn = a + (n - 1) d
Here,
- a is first term of A.P.
- n is number of terms
- d is common difference
★ We have :
- tn = 5 and 9
- n = 3 and 7
★ Applying the values in formula,
→ 5 = a + (3 - 1) d
→ 5 = a + (2) d
→ 5 = a + 2 × d
→ 5 = a + 2d {Equation No.1}
And,
→ 9 = a + (7 - 1)d
→ 9 = a + 6d {Equation No.2}
Now, we would solving both the equations and find out the value of first term (a) and common difference (d) of A.P.
Here, from Equation No.1,
→ a = 5 - 2d
Substituting it in Equation No.2,
→ 9 = (5 - 2d) + 6d
→ 9 = 5 - 2d + 6d
→ 9 = 5 + 4d
→ 4d = 9 - 5
→ 4d = 4
→ d = 4/4
→ d = 1
Finding out first term (a) :
→ a = 5 - 2d
→ a = 5 - 2
→ a = 3
Therefore,
- A.P. is 3 , 4 , 5.….