Name: General Term of an AP: Example
Uploaded: 2019-07-19
Duration: 4 min 25 s
Description: Do you know how to find the first five terms of a sequence in A.P with the help of any two given terms of the sequence? Watch this video to learn how.

Question

The sum of first seven terms of an AP is $182$ . If its $4^{t h}$ term and the $17^{t h}$ term are in the ratio $a : 5$ , find the AP.

Accepted Answer

Let $a$ be the first term and $d$ be the common difference of the $A P$ .

$∴ s_{7} = 182$

$\Rightarrow \frac{7}{2} (2 a + 6 d) = 182 (s_{n} = \frac{n}{2} [2 a + (n - 1) d])$

$\Rightarrow a + 3 d = 26 . . . (1)$

Also,

$a_{4} : a_{17} = 1 : 5$ (Given)

$\Rightarrow \frac{(a + 3 d)}{(a + 16 d)} = \frac{1}{5} [a_{n} = a + (n - 1) d]$

$\Rightarrow 5 a + 15 d = a + 16 d$

$\Rightarrow d = 4 a . . . (2)$

Solving equations $(1)$ and $(2)$ , we get

$a + 3 \times 4 a = 26$

$\Rightarrow 13 a = 26$

$\Rightarrow a = 2$

Putting $a = 2$ in (2), we get

$d = 4 \times 2 = 8$

Hence, the required $A P$ is $2, 10, 18, 26, \dots \dots \dots$

The sum of first seven terms of an AP is $182$ . If its $4^{t h}$ term and the $17^{t h}$ term are in the ratio $a : 5$ , find the AP.

Important Questions on Arithmetic Progressions

Learn and Prepare for any exam you want !

The sum of first seven terms of an AP is 182. If its 4th term and the 17th term are in the ratio a:5, find the AP.

Important Questions on Arithmetic Progressions

Learn and Prepare for any exam you want !

The sum of first seven terms of an AP is $182$ . If its $4^{t h}$ term and the $17^{t h}$ term are in the ratio $a : 5$ , find the AP.