Choose the correct alternative answer for each of the following sub questions.

In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = . . .
A. 42

B. 38

C. 21

D. 19

Attempt any two subquestions form the following:

If the second term and the fourth terms of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:

Attempt any five of the following sub questions:

Find a sequence if then find the value of S₁₀.

Attempt any two of the following subquestions:

If the sum of first p terms of an A.P. is equal to the sum of first q terms, then show that the sum of its first (p + q) terms is zero where p#q.

Attempt any two subquestions from the following:

Find the sum of all numbers from 50 to 350 which are divisible by 4. Also find 15^th term.

Attempt any four of the following subquestions:

Find the first two terms of the sequence for which S_n is given below: S_n = n² (n + 1).

If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)

Find the sum of all even numbers from 1 to 350.

Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.

(Assume the four consecutive terms in A.P. are a – d, a, a + d, a + 2d.)

In an A.P. sum of three consecutive terms is 27 and their product is 504 find the terms? (Assume that three consecutive terms in A.P. are a – d, a, a + d.)