Question

if the sum of first 6 terms of an AP is 87 and the sum of first 11 terms is 242 find the sum of n terms

Answer 1

Answer:

154 is the answer of this question

Answer 2

Answer: $\dfrac{11-3n}{2}$

Step-by-step explanation:

As we know sum of n terms of an AP is given by

$S_n=\dfrac{n}{2} (a+ (n-1)d)$

Sum of first 6 terms of AP is 87

$S_6=\dfrac{6}{2} (a+(6-1)d)\\\\\Rightarrow 87= 3(2a+5d)\\\\\Rightarrow 29=2a+5d----(i)$

Sum of 11 terms is 242

$S_{11}=\dfrac{11}{2} (2a+(11-1)d)\\\\\Rightarrow 242\times 2= 11(2a+10d)\\\\\Rightarrow 29\times 2=2a+10d\\\\\Rightarrow 29= a+5d----(ii)$

Solving (i) and (ii) we get

a=7 d= 5

Now

$S_n= \dfrac{n}{2} (2\times 7+(n-1)3)= \dfrac{n}{2} (14+3n-3) = \dfrac{11-3n}{2}$

Hence, the sum of n terms is $\dfrac{11-3n}{2}$