Question

17th terms of an ap is -4 and it's 13th term is -16.find the ap

Answer 1

Answer:

-52 , -49 , -46 ,............. ( n )

Step-by-step explanation:

t17 = -4

a + 16d = -4

t13 = - 16

a + 12d = -16

a + 16d = -4

a + 12d = - 16

( subtracting these two equations )

a + 16d - ( a + 12d ) = -4 - ( -16 )

a + 16d - a - 12d = -4 + 16

4d = 12

d = 3...

a + 12d = -16

a + 12 ( 3 ) = -16

a = -16 - 36

a = -52...

AP = a , a+d , a + 2d ,..........( n )

= -52 , -52 + 3 , -52 + 6, .........( n )

= -52, -49, -46,..........( n )

hope it helps u.............

Answer 2

✪ᴀɴsᴡᴇʀ✪

• AP is - 52, - 49, - 46,......

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

☆ɢɪᴠᴇɴ☆

• $a_{17} = - 4,\:a_{13} = - 16$

☆ᴛᴏ ғɪɴᴅ☆

• AP

᯽ғᴏʀᴍᴜʟᴀ᯽

• nth term of an AP is given by

$\:\:\:\:\:\:\:\: \star \boxed{ a_n = [ a + (n - 1)d ]} \star$

☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆

Using the above formula,

$\:\:\:\:\:\:\:\:a_{17} = - 4$

$\implies [ a + (17 - 1)d ] = - 4$

$\implies a + 16d = - 4..... (1)$

And

$\:\:\:\:\:\:\:\:a_{13} = - 16$

$\implies [ a + (13 - 1)d ] = - 16$

$\implies a + 12d = - 16..... (2)$

Substracting (2) fron (1), we get

$\: [a + 16d]-[a+12d] = - 4-(-16)$

$\implies 16d - 12d = - 4 + 16$

$\implies 4d = 12$

$\implies d = 3$

Using this value in (1), we get

$\:\:\:\:\:\:\:\: a + 16\times 3 = - 4$

$\implies a + 48 = - 4$

$\implies a = - 48 - 4$

$\implies a = - 52$

When n = 1

$\to a_1 = a$

$\to a_1 = - 52$

When n = 2

$\to a_2 = a + (2-1)d$

$\to a_2 = a + d$

$\to a_2 = - 52 + 3$

$\to a_2 = - 49$

When n = 3

$\to a_3 = a + (3-1)d$

$\to a_3 = a + 2d$

$\to a_3 = - 52 + 2\times3$

$\to a_2 = - 52 + 6$

$\to a_2 = - 46$

Thus, the AP is - 52, - 49, - 46,......