Question

In an ap if a3=9& d=3 find the value of the first term a

Answer 1

Answer:

a = 3

Step-by-step explanation:

a3 - 9

d- 3

a - ?

an = a + (n-1)d

a3= a + (3-1)3

9 = a + 6

a = 3

Answer 2

Answer:

Required first term of the seris is 3.

Step-by-step explanation:

Here given problem is in AP series.

AP series means Arithmetic Progression.

Given $a_3 = 9$

That's mean 3rd term of the series is 9.

And value of d is 3.

So,common difference of this series is 3.

We know,

$a_n = a + (n - 1)d$

Here $a_n$is the nth term ot the given series,a is the first term of the series and n is the number of term.

Here we know 3rd term of the series.

$a_3 = a + (3 - 1) \times d$

$9 = a + 2 \times 3$

$9 = a + 6$

We are separating variable and constant part,

$a = 9 - 6 = 3$

Therefore first term of the seris is 3.

By this rule we can find full series,

i.e 3,6,9,12,15,18,.........

Some others formula of AP series,

1.General from of Ap series-

a,a+d,a+2d,a+3d,.........a+nd.

2.Sum of nth term of AP series-$s = \frac{n}{2} [2a + (n - 1)d]$

3.Sum of all terms in a finite AP with the last term as "l"- $\frac{n}{2} (a + l)$