Q : 9    If the sum of first \small 7 terms of an AP is \small 49 and that of \small 17 terms is \small 289 , find the sum of
            first \small n terms.

Answers (1)

It is given that
S_7 = 49 \ and \ S_{17}= 289
Now, we know that 
S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S_{7}= \frac{7}{2}\left \{ 2\times(a) +(7-1)d\right \}
\Rightarrow 98= 7\left \{ 2a +6d\right \}
\Rightarrow a +3d = 7 \ \ \ \ \ \ \ -(i)
Similarly,
\Rightarrow S_{17}= \frac{17}{2}\left \{ 2\times(a) +(17-1)d\right \}
\Rightarrow 578= 17\left \{ 2a +16d\right \}
\Rightarrow a +8d = 17 \ \ \ \ \ \ \ -(ii)
On solving equation (i) and (ii) we will get 
a = 1 and d = 2
Now, the sum of first n terms is 
S_n = \frac{n}{2}\left \{ 2\times 1 +(n-1)2 \right \}
S_n = \frac{n}{2}\left \{ 2 +2n-2 \right \}
S_n = n^2
Therefore, the sum of n terms  is  n^2

Most Viewed Questions

Preparation Products

Knockout NEET May 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET May 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions