1)The sum of the first 6 terms of an A P is 42 The ratio of its10th to its 30"th - Maths - Arithmetic Progressions

Question

1)The sum of the first 6 terms of an A P is 42 The ratio of
its10th to its 30"th terms is1:3 Find the first term and 13th term
of the A P
2)In an A P the first term is 8 nth term is 33 and sum to first
n terms is 123 Find n and d
3)In an AP prove that am+n+am-n=2am where an denotes nth term of
the A P
4)If the sum of first m terms of an AP is n and sum of first n
terms is m,then show that the sum of first(m+n)terms is-(m+n)
5)Which term of the sequence 20, 77/4,37/2,71/3 is the first
negative term

Varun.Rawat · Accepted Answer

Refer the following links :
(1) 
https://www meritnation
com/ask-answer/question/the-sum-of-first-6-terms-of-an-a-p-is-42-the-ratio-of-its/arithmetic-progressions/3955845

(2) We have, first term, a = 8
nth term , an = 33
Sn = 123
now, an = 33
⇒a + (n - 1)d = 33
⇒ 8 + (n - 1)d = 33
⇒ (n - 1) d = 25 (1)
Sn = 123
⇒ n22a + (n - 1)d = 123
⇒n216 + (n - 1)d = 123⇒n216 + 25 = 123 [using
(1)]⇒n = 123 × 241= 6
from (1), we have
(n - 1)d = 25
5d = 25 so, d = 5

(3) 
https://www meritnation
com/ask-answer/question/1-in-an-ap-prove-that-am-n-am-n-2am-where-an-is-th/arithmetic-progressions/3618724

(4)https://www
meritnation
com/ask-answer/question/if-the-sum-of-first-m-terms-of-an-ap-is-n-and-the-sum-of-fi/arithmetic-progressions/1687556

(5) Refer the link for similar query :

https://www meritnation
com/ask-answer/question/which-term-of-the-sequence-17-161-5-152-5-143-5/arithmetic-progressions/3446548