Question

find the number of natural numbers between 100 to 1000 which are multiples of 7

Answer 1

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 ---
ᴀ= 105
d = 7
an = 994
n = ???


ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ
an = a + (n-1 )ᴅ

ꜱᴏ
994 = 105 +( n- 1) 7
994 - 105 = (n-1)7
889 /7 = n-1
127 +1 = n
n = 128

so the n = 128

☺☺hσpє ít hєlpѕ u ☺☺

♥♥fєєl frєє tσ αѕk αnч quєrч♥♥

Answer 2

hiii dear

GIVEN ---
ᴀ= 105
d = 7
an = 994
n = ???


ᴡe know that
an = a + (n-1 )ᴅ

ꜱᴏ ,
994 = 105 +( n- 1) 7
994 - 105 = (n-1)7
889 /7 = n-1
127 +1 = n
n = 128

so the n = 128