Question

If fir an ap t2=4 and d=-2 , then what is the value of a ?

Answer 1

The value of a is "6".

Step-by-step explanation:

Given,

$t_{2} =4$ and common difference(d) = - 2

To find, the first term(a) = ?

We know that,

$a_{n} =a+(n-1)d$

∴ $a_{2} =a+(2-1)d$

⇒ $a+d=4$

⇒ $a-2=4$

⇒ a = 2 + 4 = 6

Hence, the value of a is "6".

Answer 2

Given:  

In an arithmetic progression, the value of t2 is 4 and the value of the common difference is -2.  

To Find:  

The value of the first term (a) is?  

Solution:  

1. Consider an A.P having n terms with the first term a, common difference d. The nth term of the A.P is given by the formula,  

=> nth term of an A.P = Tn = a + (n-1)d,  

2. Use the above formula for the second term,  

=> t2 = a + d = 4 ( Assume as eqaution 1 ),  .  

3. Substitute the value of d in equation 1,

=> t2 = 4 = a + (d),

=> 4 = a +(-2),

=> 4 = a - 2,

=> a = 4 + 2,

=> a = 6.

=> First term = a = 6.      

5. The A.P is 6, 4, 2, 0, -2, and so on.

The value of the first term (a) is 6.