Question

Find the middle term of the Ap- 3,7,11.......83

Answer 1

hope this will help u out

Answer 2

ʜᴇyyy ᴛʜᴇʀᴇ✌✌
ᴜʀ ᴀɴꜱ ɪꜱ ʜᴇʀᴇ ----

♥Sequence = An ordered collection of numbers a1 , a2 , a3 ,............
an......is a sequence.

♥Arithmetic progression = A sequence a1,a2,a3,.........,an is called an Arithmetic progression (A.P.) when a2-a1 = a3-a3 =......an -a(n-1) . That means A.P. is a sequence in which each term is obtained by addind a constant d to the preceding term.

♥d = The constant d is called common difference of the A.P .

♥FORMULAS -----
d= a2 - a1
an = a + (n-1 )d
sn = n/2 [2a +( n-1) d]

where
a= first term of the A.P.
d = common difference
n = no of terms
an = nth term of A.p.
sn= sum to nth term

Now come to ur Question-----

GIVEN ---
a= 3
d = a2 -a1
= 7-3 = 4
an = 83
n=???
middle term???

we have to find how many term in this A.P. ---

an = a+( n-1)d
83 = 3+ ( n-1) 4
83 -3 = 4n- 4
80 + 4 = 4n
84/4 = n
n = 21

middle term = n/2
= 21/2
= 10.5

a10 = a+(n-1) d
= 3 +(10-1) 4
= 3 + 36
= 39

a11 = a+(n-1) d
=3 + ( 11-1)4
= 3+(10)4
= 3 +40
= 43

so the middle term is 39 or 43...

HOPE IT HELPS U ☺☺
ꜰᴇᴇʟ ꜰʀᴇᴇ ᴛᴏ ᴀꜱᴋ ᴀɴy qᴜᴇʀy❤❤