Question

ANSWER THIS QUESTION!!!


The sum of first 9 terms of an AP is zero and its 7th term is 10 find the sum of the first
23 terms
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Answer 1

Answer: 805

Step-by-step explanation:

The solution is in the pic. attached.

Answer 2

The sum of the first 23 terms is 805.

Given:

The sum of first 9 terms=0

7th term=10

To find:

The sum of the first 23 terms

Solution:

Let the first term of the A.P. be a and the common difference be d.

The 7th term=a+(7-1)d

10=a+6d (1)

Similarly, the sum of the first 9 terms=9/2×(2a+(9-1)d)

0=9/2×(2a+8d)

0=2a+8d

0=a+4d (2)

We will subtract (1) and (2).

a+6d-(a+4d)=10-0

a+6d-a-4d=10

2d=10

d=5

Putting d=5 in (2),

0=a+4×5

0=a+20

a= -20

So, the sum of the first 23 terms=23/2×(2a+(23-1)d)

Using the values of a and d,

=23/2×(2(-20)+22×5)

=23/2×(-40+110)

=23/2×70

=23×35

=805

Therefore, the sum of the first 23 terms is 805.