1.} Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
2.} If the sum of the first 7 terms of an A.P. is 119 and that of the first 17 terms is 714, find the sum of its first n terms.
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Answers
Answer1
2 is the common difference of an AP
Given:
a (first term of the arithmetic progression) = 5
To find:
d (Common Difference) = ?
Solution:
The general sequence of an AP is a ,a + d ,a + 2d ,a + 3d,…
Substituting a=5 then
5, 5 + d,5 + 2d,5 + 3d,5 + 4d,5 + 5d,5 + 6d,5 + 7d,,..
Let the first 4 terms be 5,5 + d,5 + 2d,5 + 3d
And let the next 4 terms be = 5 + 4d,5 + 5d,5 + 6d,5 + 7d
And
By substituting these values in (1)
20+6d=10+11d
10=5d
d=2
Therefore, the common difference = 2
Answer 2
HERE,
according to question,
CASE 1
S7=n/2[2a+(n-1)d]
119=n/2[2a+(6)d]
238=14a+42d
119=7a+21d
CASE-2
S17=n/2[2a+(n-1)d]
714=17/2[2a+(16)d]
1428=34a+270d
714=17a+135d
therefore,
by elimination method we get ,
Or
The sum of n terms is
Step-by-step explanation:
Given : If the sum of first 7 terms of an AP is 119 and that of the first 17 terms is 714.
To find : The sum of its first n terms?
Solution :
The sum formula is,
For 7 terms,
......(1)
For 17 terms,
.....(2)
Now, subtracting (1) from (2), we get.
Substituting the value d = 4 in equation (2), we get.
Now, substitute a=5 and d=4
Therefore, The sum of n terms is Sn = 3n + 2n^2
Answer:
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