If the sum of first 7 terms of an A.P is 49 and the sum of first 17 terms is 289 find the sum of first 30 term

Answers

Answer 1
Given:

Sum of first 7 terms of an AP = 49.

Sum of first 17 terms = 289

Find:

the sum of first 30 term

Solution:

We know that,

Sum of first n terms of an AP – S(n) = n/2 * [ 2a + (n - 1)d ]

Hence,

→ 7/2 * [ 2a + (7 - 1)d ] = 49

→ 2a + 6d = 49 * 2/7

→ 2( a + 3d ) = 14

→ a + 3d = 14/2

→ a + 3d = 7 -- equation (1)

Similarly,

→ 17/2 * [ 2a + 16d ] = 289

→ 17/2 * 2 * (a + 8d) = 289

→ a + 8d = 289 * 2/17 * 1/2

→ a + 8d = 17 -- equation (2)

Subtract equation (1) from (2).

→ a + 8d - (a + 3d) = 17 - 7

→ a + 8d - a - 3d = 10

→ 5d = 10

→ d = 10/5

→ d = 2

Substitute the value of d in equation (1).

→ a + 3 * 2 = 7

→ a = 7 - 6

→ a = 1

Now,

Sum of first 30 terms = 30/2 * [ 2(1) + (30 - 1)(2) ]

→ S(30) = 15 (2 + 58)

→ S(30) = 15 * 60

→ S(30) = 900

Therefore, the sum of first 30 terms of the given AP is 900.

I hope it will help you.

Regards.

Answer 2

answer refer in pic siso

If The Sum Of First 7 Terms Of An A.P Is 49 And The Sum Of First 17 Terms Is 289 Find The Sum Of First
If The Sum Of First 7 Terms Of An A.P Is 49 And The Sum Of First 17 Terms Is 289 Find The Sum Of First

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