Name: How to Identify Missing Number in the Sequence?
Uploaded: 2019-07-19
Duration: 14 min 44 s
Description: Let's observe the pattern in the given number of terms that follow some sequence and find out the missing term. Use your logic and try to solve it.

Question

The sum of first seven terms of an A.P. is

182

. If its

4^{th}

and

17^{th}

terms are in the ratio

1 : 5

, find the A.P.

Accepted Answer

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

We know that sum of $n$ terms of an A.P. is $1 : 5$ .

Given that the sum of the first seven terms of an A.P. is $S_{7} = 182$ .

$S_{7} = \frac{7}{2} [2 a + (7 - 1) d]$

$182 = \frac{7}{2} [2 a + 6 d] . . . . . . . . . . . (i)$

We know that $n^{th}$ term of an A.P. is $a_{n} = a + (n - 1) d$ .

Given that its $4^{th}$ and $17^{th}$ terms are in the ratio $1 : 5$ that is $\frac{t_{4}}{t_{17}} = \frac{1}{5}$ .

$1 : 5$

$\Rightarrow \frac{a + 3 d}{a + 16 d} = \frac{1}{5}$

$\Rightarrow 5 (a + 3 d) = a + 16 d$

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

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

Substituting equation $(i i)$ in the equation $(i)$ , we get,

$\Rightarrow 182 = \frac{7}{2} [2 a + 6 \times 4 a]$

$\Rightarrow 364 = 7 \times 26 a$

$\Rightarrow 52 = 26 a$

$\Rightarrow a = 2$

Hence, the first term of an A.P. is $a = 2$ .

Substituting $a = 2$ in the equation $(i i)$ , we get,

$d = 4 \times 2 = 8$ .

Hence, common difference of an A.P. is $8$ .

Now, we know the general form of an A.P. is $a, a + d, a + 2 d, a + 3 d, . . .$

Therefore, $2, 2 + 8 = 10, 2 + 2 \times 8 = 18, 2 + 3 \times 8 = 26, . . .$

Hence, A.P. is $2, 10, 18, 26, . . . .$

The sum of first seven terms of an A.P. is $182$ . If its $4^{th}$ and $17^{th}$ terms are in the ratio $1 : 5$ , find the A.P.

Important Questions on Arithmetic Progressions

Learn and Prepare for any exam you want !

The sum of first seven terms of an A.P. is 182. If its 4th and 17th terms are in the ratio 1:5, find the A.P.

Important Questions on Arithmetic Progressions

Learn and Prepare for any exam you want !

The sum of first seven terms of an A.P. is $182$ . If its $4^{th}$ and $17^{th}$ terms are in the ratio $1 : 5$ , find the A.P.