Question

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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Answer 1

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 2

Answer:

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