Let there be an A.P. with first term ' a ', common difference ' d… - Vidyadip

Question

Let there be an A.P. with first term ' $a$ ', common difference ' $d$ '. If $a_n$ denotes in $n^{\text {th }}$ term and $S_n$ the sum of first $n$ terms,
find. $k$, if $S _{ n }=3 n ^2+5 n$ and $ak =164$.

✓

Answer

$a_k=S_k-S_{k-1}$
$\Rightarrow 164=\left(3 k^2+5 k\right)-\left(3(k-1)^2+5(k-1)\right)$
$\Rightarrow 164=3 k^2+5 k-3 k^2+6 k-3-5 k+5$
$\Rightarrow 164=6 k+2$
$\Rightarrow 6 k=162$
$\Rightarrow k=27$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Arithmetic Progressions→Arithmetic Progressions — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Prove the following trigonometric identities.
$\frac{(1+\cot^2\theta)\tan\theta}{\sec^2\theta}=\cot\theta$

Write the correct alternative for the following question.
What is the amount of dividend received per share of face value Rs. 10 and dividend declared is 50%.

In an A.P. the 10th term is 46, sum of the 5th and 7th term is 52. Find the A.P.

In figure 1.73, ∠ABC = ∠DCB = 90° AB = 6, DC = 8 then $\frac{ A (\triangle ABC )}{ A (\triangle DCB )}=?$

→

If two dice are rolled simultaneously, find the probability of the following events.
The sum of the digits on the upper faces is at least 10.

Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions,
find out the common difference.
$0, -4, -8, -12$, .....

Prove that $(\sin32^\circ\cos58^\circ+\cos32^\circ\sin58^\circ)=1.$

Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonals is 26 cm, find the length of the other.

Find the simplest form of:$\frac{368}{496}$

Solve the following simultaneous equation.
99x + 101 y = 499; 101x + 99y = 501