This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6
In this question we have been given that In an A.P. the first term is 8, nth term is 33 and the sum of first n terms is 123.
Now we have to find n and the d, the common difference.
CBSE DHANPAT RAI publications
Class:- 10th
Solutions of CBSE Mathematics
Question 24
Given A.P. has first term(a) = 8, nth term(an) = 33 and sum(Sn) = 123.
We know sum of n terms of an A.P. is given by, Sn = n[a + an]/2
=> 123 = n[8 + 33]/2
=> 41n = 246
=> n = 6
Also, we know nth term of an A.P. given by, an = a + (n − 1)d.
=> 33 = 8 + (6 − 1)d
=> 5d = 25
=> d = 5
Hence, the number of terms of given A.P. is 6 and common difference is 5