Question

find the sum of an ap whose middle most term is 30

Answer 1

Answer:

The sum of the AP is 330

Step-by-step explanation:

The complete question is

Find the sum of the 11 terms of an AP whose middle most term is 30.

Solution:

No. of terms in the AP = 11

Then the middle term will be 6th term

If the first term of the AP is a and common difference d then

The nth term of the AP is given by

$a_n=a+(n-1)d$

Given

$a_6=30$

$\implies a+(6-1)d=30$

$\implies a+5d=30$

Now the sum of the 11 terms of AP is given by

$S=\frac{11}{2}[2a+(11-1)d]$

$\implies S=\frac{11}{2}[2a+10d]$

$\implies S=\frac{11}{2}\times 2[a+5d]$

$\implies S=\frac{11}{2}\times 2\times 30$

$\implies S=330$

Therefore the sum of the AP is 330.

Answer 2

Answer:

answer is 330

Step-by-step explanation:

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