Question

How many terms are there in the A.P. 41, 38, 35, ......., -1?

Answer 1

Answer:

Given :

• a = 41
• d = 38-41 = -3
• an = -1

To find :

• n = ?

Solution :

an = a + (n - 1)d

➸ -1 = 41 + (n - 1)(-3)

➸ -1 = 41 - 3n + 3

➸ 3n = 41 + 1 + 3

➸ 3n = 45

➸ n = 45/3

➸ n = 15

So, -1 is the 15th term of the given arithmetic progression.

SOME FORMULAS :

➸ An = A + (n - 1)d

➸ Sn = n/2(2a + (n - 1)d)

➸ Ln = L - (n - 1)d

➸ Sn = n/2(a + l)

➸ An arithmetic progression is a series in which every term has a difference of some number between them.

➸ This difference is called common difference. And is represented by d.

➸ The first term of the arithmetic progression is represented by a.

➸ The number of terms in the arithmetic progression is represented by n.

Answer 2

AnsweR :-

Given

• First term ( a ) = 41
• tn = - 1

To FiNd :-

• n = ?

SoLuTiOn :-

Firstly finding common difference ( d )

Common difference ( d ) = t₂ - t₁

d = 38 - 41

d = - 3

Using

♦ tn = a + (n - 1)d

Substituting the values of tn , a & d

→ - 1 = 41 + (n - 1)( - 3)

→ - 1 - 41 = - 3n + 3

→ - 45/- 3 = n

n = 15

Hence, number of terms in A.P = 15