0
Find the sum of an arithmetic progression of seventeen terms whose middle term is 5?
85 (=17*5).
The middle term is 5. There are 8 terms bigger than 5 and 8 smaller.
The term smaller than 5 and next to it is 5 - r
The term bigger than 5 and next to it is 5 + r
So these two average 5.
Similarly, the next pair outwards average 5; and so on.
So the sum of the progression is equivalent to the sum of 8 pairs of numbers whose average is 5 and the middle term which is 5 ie 17 lots of 5.
Still curious? Ask our experts.
Chat with our AI personalities
Blake
Professor
JordanAdd your answer:
Earn +20 pts
What is an arithmetic series?
An arithmetic series is the sum of the terms in an arithmetic progression.
Who gave the formula for finding sum of the first 'n' terms in Arithmetic Progression?
RAMANUJANRAMANUJAN
The 7th term of an arithmetic progression is 6 The sum of the first 10 terms is 30 Find the 5th term of the progression?
2
What is the sum of the first 15 terms of an arithmetic?
For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.
Is -2-6-18-54-162-468-1458 geometric or arithmetic?
It is neither. (-6) - (-2) = -4 (-18) - (-6) = -12 which is not the same as -4. Therefore it is not an arithmetic progression - which requires the difference between successive terms to be the same. Also -162/-54 = 3 -468/-162 = 2.88... recurring, and that is not the same as 3. Therefore it is not a geometric progression - which requires the ratio of terms to be the same.
