if the first term of the Ap is 1 and common difference is 4 ,then which term of the Ap is 77​

2 thoughts on “if the first term of the Ap is 1 and common difference is 4 ,then which term of the Ap is 77​”

1. Given:-

   • First term of the A.P is 1 and common difference is 4.

   To Find:–

   • 77 is which term of the given A.P.

   Formula Used:–

   • [tex]{\boxed{\bf{a_n=a+(n-1)d}}}[/tex]

   Solution:–

   Using, [tex]\bf a_n=a+(n-1)d[/tex]

   Here,

   • [tex]\bf a_n = 77[/tex]

   • a = 1

   • d = 4

   Putting Values,

   [tex]\sf :\implies\:77=1+(n-1)4[/tex]

   [tex]\sf :\implies\:77=1+4n-4[/tex]

   [tex]\sf :\implies\:77=4n-3[/tex]

   [tex]\sf :\implies\:4n=77+3[/tex]

   [tex]\sf :\implies\:n=\dfrac{80}{4}[/tex]

   [tex]\bf :\implies\:n=20[/tex]

   Hence, 77 is the 20th term of the given A.P.

   ━━━━━━━━━━━━━━━━━━

   More Formulas related to A.P:–

   • [tex]\bf S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

   • [tex]\bf S_n=\dfrac{n}{2}[a+a_n][/tex]

   • [tex]\bf S_n=\dfrac{n}{2}[a+l][/tex]

   ━━━━━━━━━━━━━━━━━━

   Reply

2. Answer :

   • 20th term of the A.P. is 77.

   Given :

   • First term (a) = 1.
   • Common difference (d) = 4.

   To Find :

   • Which term of the A.P. is 77.

   Solution :

   We have,

   • a = 1

   • d = 4

   • aₙ = 77

   • n = ?

   We have to find the n.

   We know that,

   ★ aₙ = a + (n – 1)d

   Now, substitute all the given values in the formula.

   => 77 = 1 + (n – 1)(4)

   => 77 = 1 + 4n – 4

   => 77 = 4n – 3

   => 77 + 3 = 4n

   => 80 = 4n

   => 80/4 = n

   => 20 = n

   => n = 20

   Hence,

   20th term of the A.P. is 77.

   Verification :

   Now we have,

   • a = 1

   • d = 4

   • aₙ = 77

   • n = 20

   Substitute all the values in the formula.

   Formula : aₙ = a + (n – 1)d

   => 77 = 1 + (20 – 1)(4)

   => 77 = 1 + (19)(4)

   => 77 = 1 + 76

   => 77 = 77

   L.H.S. = R.H.S.

   Hence Verified.

   Reply