Question

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

Answer 1

here you go ☆☆

given:-

▪a = 3
▪d = 7 - 3 => 4
▪a(n) = 83

□to find middle term

a(n) = $a + (n - 1)d$

▪$83 = 3 + (n - 1)4$

▪$80 = (n - 1)4$

▪$n - 1 = \frac{80}{4}$

▪$n - 1 = 20 = > 20 - 1 \\ n = 19$

■middle term is 10th term

▪a(10) =>
▪3 + 9(4)
▪3 + 36
▪39

hope it helps:)

Answer 2

HEYY THERE
UR ANS IS HERE


♥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


so the middle term is 39...


HOPE IT HELPS U ☺☺