What is the sum of the first 8 terms of the series: 11, 18, 25, 32...
5 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
11, 18, 25, 32, ..., a8
we notice that we have an A.P where a1= 11 and r= 7
a1= 11
a2= 11+7 = 18
a3= 11+7*2 = 25
a4 = 11+ 7*3= 32
a5= 11 + 7*4= 39
a6 = 11+ 7*5 = 46
a7 = 11+ 7*6 = 53
a8 = 11 + 7*7 = 60
Then the sum is:
S = 11 + 18 + 25 + 32 + 39 + 46 + 53 + 60 = 284
Then the sum = 284
giorgiana1976 | College Teacher | (Level 3) Valedictorian
We'll apply the formula of the sum of the n terms of an arithmetic sequence:
Sn = (a1+an)*n/2
Now, we'll substitute n by 8:
S8 = (a1 + a8)*8/2
S8 = (a1 + a8)*4
We'll know the value of the first 4 terms from the 8 terms.
But we know the formula of finding any term of an arithmetic series.
an =a1 + (n-1)*d, where a1 is the first term and d is the common difference.
a8 = a1 + (8-1)*d
We could calculate d from:
a2 - a1 = d
18 - 11 = 7
d = 7
a8 = 11 + 7*7
a8 = 11 + 49
a8 = 60
S8 = (11 + 60)*4
S8 = 71*4
S8 = 284
The sum of the first 8 terms of the arithmetic progression, whose first term is 11 and common difference is 7, is S8 = 284.
neela | High School Teacher | (Level 3) Valedictorian
To find the sum of the 1st 8 terms of 11,18,25,32...
Solution:
We check for the difference:
ar = rth term.
a2-a1 = 18 - 11 = 7.
a3-a2 = 25 - 18 = 7.
a4-a2 = 32 - 25 = 7.
We conclude that this is an arithmrtic progression with starting term a1 = 11 and the common difference d = 7 between the cosecutive terms.
So the sum of n terms is given by:
Sn = (a1+an)d/2.
In our examle,
a1 = 11.
a8 = 11+(8-1)*7 = 11+7*7 = 60.
S8 = {11+60}8/2 = 71*4 = 284.
william1941 | College Teacher | (Level 3) Valedictorian
Looking as the series, we see that 18 - 11= 25 - 18= 32- 25 =7.
So we see that it is an AP with the common difference equal to 7 and the first term equal to 11.
For an AP, the nth term is expressed as a+(n-1)*d where a is the first term and d is the common difference.
Also the sum of n terms of an AP is (n/2)*(2a+(n-1)d).
Substituting the values we have here:
(n/2)*(2a+(n-1)d)= (8/2)* ( 2*11 + 7* 7)
= 4 *( 22+49)
=4*71
= 284
The sum of the first 8 terms of the series is 284
eyitopps4real | Student, Undergraduate | (Level 1) eNoter
It is an arithmetic progression whose common difference is 7 (difference between two consecutive terms). The formula for the sum of an A.P is SUM = n/2 [2a + (n - 1)d]. From the question, n = 8 (i.e number of terms), a = 11 ( the first term), and d = 7 ( common difference). Substituting into the equation for sum of an A.P we obtain SUM = 8/2 [2 * 11 + (8 - 1)7]. ==> SUM = 4 [22 +49] ==> SUM = 4 * 71 ==> SUM = 284