# Show that the sum of all terms of an A.P. whose first term is a

## Question 7:

Show that the sum of all terms of an A.P. whose first term is a, the second term is b and the last term is c is equal to .                                                    [CBSE      2020]

### Solution:

Given first term , Second term and last term l = c.

So, common difference,

Let this A.P. contains n terms.

Then,  l = a + (n – 1)d

⇒ c = a + (n – 1)(b – a)

⇒ c – a = (n – 1)(b – a)

………(i)

⇒ Now, sum of n terms of A.P. is given by.

[Using (i)]

Hence, proved

## Question 1:

Ramkali would require Rs 5000 for getting her daughter admitted in a school after a year. She saved Rs 150 in the first month and increased her monthly by Rs 50 every month. Find, if she will be able to arrange the required money after 12 months. Which value is reflected in her efforts ?

## Question 2:

The first term of an A.P. is -5 and the last term is 45. If the sum of  the terms of the A.P. is 120, then find the number of terms and the common difference.

## Question 3:

If the sum of the first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of the first 10 terms.

[CBSE 2016, 13, 12]

## Question 4:

The digits of a positive number of three digits are in A.P.  and  their sum is 15. The number obtained by reversing the digits  is 594 less than the original number. Find the number.

## Question 5:

If the sum of first m terms of an A.P. is some as the sum of its first n terms, show that the sum of its first (m + n) terms is zero.                          [CBSE  2019]

## Question 6:

If the sum of first ‘p’ terms of an A.P. is ‘q’ and the sum of first ‘q’ terms is ‘p’ ; then show that the sum of the first (p + q) terms is {-(p + q)}.

## Question 8:

Yasmeen saves ₹ 32 during the first month ₹ 36 in the second month and ₹ 40 in the third month. If she continues to save in this manner, in how many months will she save ₹ 2000?