For an AP, it is given that:Last term (I) = 28. S = 144, and
there are total 9 terms. Find the first term.
3
14
5
6
Answers
Answer:Answer is 4
Step-by-step explanation:
the formulae for sum of AP with n terms, first term P and last term Q is
= n*(P + Q)/2
144=9*(28+P)/2
32=28+P
P=4
Thanks hope it helps.
Answer :
a = 4
Note :
★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.
★ If a1 , a2 , a3 , . . . , an are in AP , then
a2 - a1 = a3 - a2 = a4 - a3 = . . .
★ The common difference of an AP is given by ; d = a(n) - a(n-1) .
★ The nth term of an AP is given by ;
a(n) = a1 + (n - 1)d .
★ If a , b , c are in AP , then 2b = a + c .
★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .
★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .
★ A linear polynomial in variable n always represents the nth term of an AP .
★ A quadratic polynomial in variable n always represents the sum of n terms of an AP .
★ If each terms of an AP is multiplied or divided by same quantity , then the resulting sequence is an AP .
★ If same quantity is added or subtracted in each term of an AP then the resulting sequence is an AP .
Solution :
- Given : last term , l = 28 , S(9) = 144
- To find : First term , a = ?
We know that ,
The sum of first n terms of an AP is given as ;
S(n) = (n/2)×( a + l ) , where a is the first term and l is the last term of the AP .
Thus ,
=> S(n) = (n/2)×(a + l)
=> S(9) = (9/2)×(a + l)
=> 144 = (9/2)×(a + 28)
=> 144×2 = 9×(a + 28)
=> 288 = 9a + 252
=> 9a = 288 - 252
=> 9a = 36
=> a = 36/9
=> a = 4