Question

if sum of n terms of two AP are in ratio (2n+1):1 then ratio of 4th terms will be?​

Answer 1

Answer:

so fourth term is 9

Step-by-step explanation:

WHEN n=1

ratio = 3:1

when n= 2

ratio=5:1

when n=3

ratio= 7:1

so when n= 4

ratio = 9:1

Answer 2

Step-by-step explanation:

Given: if sum of n terms of two AP are in ratio (2n+1):1.

To find: Ratio of 4th terms will be ?

Solution:

Formula to be used:

1)Sum of n terms of AP:$\bf S_n = \frac{n}{2} (2a + (n - 1)d)$

2) nth term of AP: $\bf a_n = a + (n - 1)d$

Here,

a is first term, d is common difference and n is number of terms in the AP.

Step 1:Write the given ratio of sum of n terms

Let $a_1$ and $d_1$ are the first term and common difference of AP1 respectively and $a_2$ and $d_2$ are the first term and common difference of AP2 respectively.

$\frac{S1_{n}}{S2_{n}} = \frac{\frac{n}{2} (2a_1 + (n - 1)d_1)}{\frac{n}{2} (2a_2 + (n - 1)d_2)}$

cancel common terms

$\frac{ 2a_1 + (n - 1)d_1}{ 2a_2 + (n - 1)d_2} = \frac{2n + 1}{1}$

Step 2: Assume the value of n, so that the LHS will be the 4th term

4th term: a+3d

Put n=7

$\frac{ 2a_1 + (7 - 1)d_1}{ 2a_2 + (7 - 1)d_2} = \frac{2 \times 7 + 1}{1}$

or

$\frac{ 2a_1 + 6d_1}{ 2a_2 + 6d_2} = \frac{14 + 1}{1}$

cancel common factors

$\frac{ a_1 + 3d_1}{ a_2 + 3d_2} = \frac{15}{1}$

or

$\frac{ a1_4}{ a2_4} = \frac{15}{1}$

Final answer:

Ratio of 4th terms is both AP's are 15:1

Hope it will help you.

Learn more:

1) The sum of first n terms of an arithmetic progression is 210.and sum of its first n-1 terms is 171.if the first term is ...

https://brainly.in/question/12304646

2) यदि किसी A.P. के प्रथम 7 पदों का योग 49 है और प्रथम 17 पदों का योग 289 है, तो इसके प्रथम n पदों का योग ज्ञात कीजिए।

https://brainly.in/question/6623360

3)6, 10, 14 are in Arithmetic progression Find its 15th term.

https://brainly.in/question/40882455