Question

in an ap the first term is 8 ,nth term is 33 and sum to first n terms is 123 find n and d, common differences

Answer 1

n = 6, d= 5. This is the answer (A picture of the solution is also attached)

Answer 2

Answer:

n = 5,

d = 6

Explanation:

It is given that ,

In an A.P :

First term (a) = 8,

$n^{th}\: term = a_{n}=33$

and

Sum of first n terms =

$S_{n} = 123$

i) $S_{n}=123$

$\implies \frac{n}{2}[a+a_{n}]=123$

$\implies\frac{n}{2}[8+33]=123$

$\implies \frac{41n}{2}=123$

$\implies n = \frac{2\times123}{41}$

$\implies n = 2 \times 3$

Therefore,

$n = 6$ ---(1)

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

substitute a = 8 and n = 6, we get

$\implies 8+(6-1)d=33$

$\implies 8+5d = 33$

$\implies 5d = 33-8$

$\implies 5d = 25$

$\implies d = \frac{25}{5}$

$\implies d = 5$

Therefore,

n = 6,

d = 5

•••