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