Question

sum of first 49 terms of an ap is 1274 find its 25th term​

Answer 1

Answer:

25th term is 26

Step-by-step explanation:

S49=1274

by formula,

Sn = n/2[2a+(n-1)d]

1274=49/2[2a+(49-1)d]

1274×2=49[2a+48d]

2548/49=2a+48d

52=2a+48d

multiply 2 to both sides

26=a+24d____(1)

n=25

tn=a+(n-1)d

t25=a+(25-1)d

t25=a+24d

t25=26

Answer 2

Answer:

The 25th term of the A.P is t₂₅ = a+24d = 26

Option (C) is correct.

Step-by-step explanation:

Arithmetic progression:

• Arithmetic progression is a sequence of numbers in order, where the difference between any two consecutive numbers is constant.

• The Arithmetic progression is shortly denoted by A.P

• The terms in A.P are in the form of

           a, a+d, a+2d, a+3d,.........

          where a is the first term

           d is the difference between the terms

          nth term of A.P = tₙ = a+(n-1)d

           Sum of n terms = Sₙ = (n/2)[2a+(n-1)d]

• Given,

         Sum of first 49 terms S₄₉ = 1274

         Sum of first n terms = Sₙ = (n/2)[2a+(n-1)d]

                   here n = 49

             S₄₉ = (49/2)[2a+(49-1)d]

           1274 = (49/2)[2a+48d}

           1274 = (49/2)2(a+24d)

           1274 = 49(a+24d)

        1274/49=a+24d

                26 = a+24d

           a+24d = 26      -------------(i)

  Since the 25th term = t₂₅ = a+24d -----------(ii)

   By equating (i) and (ii) we get the 25th term

   Hence, 25th term =   t₂₅ = a+24d = 26

Know more about Arithmetic progression:

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