If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is
1 point
0
6
15
9
Answers
Answer :
1st Option : 0
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 ] .
or S(n) = (n/2)×(a + l) , l is the last term .
★ 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 :
Here ,
In an AP we have ;
• First term , a1 (or a) = -5
• Common difference = 2
To find :
• S(6)
Now ,
We know that , sum of n terms of AP is ;
S(n) = (n/2)×[ 2a + (n - 1)d ]
Thus ,
The sum of 6 terms of the AP will be ,
=> S(6) = (6/2)×[ 2•(-5) + (6 - 1)•2 ]
=> S(6) = 3×[ -10 + 5•2 ]
=> S(6) = 3×[ -10 + 10 ]
=> S(6) = 3×0
=> S(6) = 0
Hence ,
Required sum , S(6) = 0
(1st option)
Answer:
Option a) 0
Step-by-step explanation:
Given; first term (a) is -5, common difference (d) is 2 and number of terms (n) is 6.
We have to find the sum of the first 6 terms.
We know that-
Sn = n/2 [2a + (n - 1)d]
Substitute the values,
→ S(6) = 6/2 × [ 2(-5) + (6 - 1)2 ]
→ S(6) = 3 (-10 + 5(2))
→ S(6) = 3 (-10 + 10)
→ S(6) = 3(0)
→ S(6) = 0
Hence, the sum of the first 6 terms is 0.