Question

if sum of n terms of AP 2,5,8 is 155 then the number of terms is

Answer 1

[tex]Sn = \frac{n}{2} (2a+(n-1)d) Given Sn=155, a=2,d=3,
⇒155= \frac{n}{2}(3n+1) [/tex]
⇒[tex]310=3n^2+n
⇒n=10[/tex]

Answer 2

Answer:

10

Step-by-step explanation:

A.P. = 2,5,8...

First term = a = 2

Common difference = d= 5-2=8-5=3

Sum of first n terms in A.P. : $S_n=\frac{n}{2}(2a+(n-1)d)$

We are given that sum of n terms is 155

Substitute the values

$155=\frac{n}{2}(2(2)+(n-1)3)$

$155=\frac{n}{2}(4+3n-3)$

$310=n+3n^2$

$3n^2+n-310=0$

$(n-10)(3n+31)=0$

$n=10,-\frac{31}[2}$

Since number of terms cannot be negative

So, n = 10

Hence the number of terms is 10