Q : 10   Show that  \small a_1,a_2,...,a_n,...  form an AP where an is defined as below :

               (i)   \small a_n=3+4n

               Also find the sum of the first \small 15 terms .

Answers (1)

It is given that 
\small a_n=3+4n
We will check values of a_n for different values of n
a_1 = 3+4(1) =3+4= 7
a_2 = 3+4(2) =3+8= 11
a_3 = 3+4(3) =3+12= 15
and so on.
From the above, we can clearly see that this is an AP with the first term(a) equals to and common difference (d) equals to 4
Now, we know that 
S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S_{15}= \frac{15}{2}\left \{ 2\times(7) +(15-1)4\right \}
\Rightarrow S_{15}= \frac{15}{2}\left \{ 14 +56\right \}
\Rightarrow S_{15}= \frac{15}{2}\left \{ 70\right \}
\Rightarrow S_{15}= 15 \times 35
\Rightarrow S_{15}= 525
Therefore, the sum of 15 terms  is  525

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