Question

The 5th term of



a.P is 1whereas its 31 term is -77 which term of the



a.P is -17

Answer 1

Given

• 5th term = 1
• 31st term = - 77

→ 5th term = a + 4d = 1 _(1)

→ 31st term = a + 30d = - 77 _(2)

By doing (2) - (1) we get,

→ 26d = - 78

→ d = - 3

Hence by substituting value we get,

→ a + 4(- 3) = 1

→ a = 13

To Find

nth term having value of - 17

→ - 17 = 13 + (n - 1)(- 3)

→ - 30 = - 3(n - 1)

→ 10 + 1 = n

→ 11 = n

Hence 11th term in A.P., is - 17.

Answer 2

Answer:-

11th term

Explanation:-

Given

In an A.P.

5th term is 1

31st term is -77

To Find:

The term which has the value -17

Solution

Let,

First term of the AP is a

Common difference = d

Now

5th term = a+4d = 1 ----(1)

31st term = a+30d = -77 ------(2)

Subtract (1) from (2),

(a+30d)-(a+4d) = -77-1

a+30d-a-4d = -78

26d = -78

d = -78/26

d = -3

sub. d = -3 in eq.(1)

a+4(-3) = 1

a-12 = 1

a = 1+12

a = 13

__________________

We have

a = 13

d = -3

an = -17

We know that

$\boxed{an = a+(n-1)d }$

on putting values

-17 = 13+(n-1)(-3)

-17 = 13-3n+3

-17 = 16-3n

3n = 16+17

3n = 33

n = 33/3

n = 11

Hence,

-17 is the 11th term of the AP