kth term of an AP is 4k+1.
write the 1st term and common differnce.
find the sum of 1st 25 terms​

1 thought on “kth term of an AP is 4k+1.<br />write the 1st term and common differnce.<br />find the sum of 1st 25 terms​”

1. Step-by-step explanation:

   Given :–

   kth term of an AP is 4k+1.

   To find :–

   Write the 1st term?

   Write common difference ?

   Find the sum of 1st 25 terms ?

   Solution :–

   Given that :

   kth term of an AP = 4k+1

   ak = 4k+1 ————-(1)

   Put k = 1 then

   a1 = 4(1)+1

   => a1 = 4+1

   => a1 = 5

   First term = 5

   Put k = 2 then

   a2 = 4(2)+1

   => a2 = 8+1

   =>a2 = 9

   Common difference = a2 – a1

   => d = 9-5

   => d = 4

   Common difference = 4

   We know that

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

   We have ,

   a = 5

   d = 4

   n = 25

   On Substituting these values in the above formula then

   => Sum of first 25 terms

   => S 25 = (25/2)[2(5)+(25-1)(4)]

   => S 25 = (25/2)[10+24(4)]

   =>S 25 = (25/2)[10+96]

   =>S 25 = (25/2)(106)

   => S 25 = (25×106)/2

   => S 25 = 25×53

   => S 25 = 1325

   Answer:–

   i) First term of the AP = 5

   ii) Common difference of the AP = 4

   ii) Sum of first 25 terms of the AP = 1325

   Used formulae:–

   • The sum of first n terms of an AP
   • = Sn = (n/2)[2a+(n-1)d]
   • a = First term
   • d = Common difference
   • n= number of terms

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