Question

n terms lie between 7and 49 is an AP.if ratio of the fourth term and the (n-1)th Term is 5:4, then find the value of n

Answer 1

Answer:

1:7

Step-by-step explanation:

u just have to multiply it's easy yo look 7x7=49 n 7x1=7 it's easy

Answer 2

Solution

First term a = 7

In between 7 and 49 there is n arithmetic mean.

$∴ \: \: 49 = (n + 2 {)}^{th} term$

$➛a + (n + 1)d$

$➛7 + (n + 1)d$

$⟹49 - 7 = (n + 1)d$

$⟹(n + 1)d = 42$

$∴ \: \: \: d = \frac{42}{n + 1}$

Fourth mean term = fifth term

$⟾a + 4d$

$⟾7 + 4d$

$(n - 2 {)}^{th} mean \: term = (n - 1 {)}^{th} term.$

$⟾a + (n - 2)d$

$⟾7 + (n - 2)d$

According to question,

$\frac{fourth \: mean \: tern}{(n - 2 {)}^{th} \: mean \: term } = \frac{5}{4}$

$⟾ \frac{7 + 4d}{7 + (n - 2)d} = \frac{5}{4}$

$⟾35 + 5(n - 2)d = 28 + 16d$

$⟾35 - 28 = 16d - (5n - 10)d$

$⟾7 =( 16 - 5n + 10 )d$

$⟾7 = (26 - 5n). \frac{24}{n + 1} ,$

Formula

${∴d = \frac{42}{ n+ 1 }}$

$⟹n + 1 = (26 - 5n).6$

$⟹n = 156 - 30n - 1$

$⟹n + 30n = 155$

$31n = 155$

$∴n = \frac{155}{31} = 5.$