Question

an=4 d=2 sn=-15 find n and a

Answer 1

Answer:

Your answer is here........

n=2

a=2

Answer 2

The first term is a=-8 and number of terms is n=7.

Step-by-step explanation:

Given : $a_n=4, d=2,\ s_n=-15$

To find : The value of n and a ?

Solution :

nth term in the AP $a_n = 4$,

Common difference (d) = 2

Sum of the series is $s_n = -14$

$a_n = a +(n-1)d$  

$4 = a + (n-1)2$

$6 = a + 2n$

$a = 6-2n$   .....(1)

Sum of the series $S_n=\frac{n}{2}[2a + (n-1) d]$

$-14=\frac{n}{2}[ 2\times (6-2n) + (n-1)2]$

$-14 = n[5-n]$

$n^2 -5n -14 = 0$

$n^2 -7n + 2n -14 = 0$

$n(n-7) + 2(n-7) = 0$

$(n-7)(n+2) = 0$

$n-7 = 0\Rightarrow  n = 7 \text{ (or) } n+2 = 0\Rightarrow n -2$

Since n should be a positive integer.

So we take n = 7

Substitute in equation (1),

$a = 6-2n$

$a = 6-2(7)$

$a =-8$

The first term is a=-8 and number of terms is n=7.

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