Question

if -22 is the nth term of arithmetic progression 5,2,-1....... then n = ?

answer = 10

need explanation​

Answer 1

5,2,-1,-4,-7

ᴅ=ᴀ2-ᴀ1=2-5= -3

ᴀ=5

ᴀɴ = ᴀ + (ɴ-1)ᴅ = 0

-22 = 5 + (ɴ-1)-3

-22 -5 = -3ɴ+3

-30 = -3ɴ

10 = ɴ

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Answer 2

Answer- The above question is from the chapter 'Arithmetic Progressions'.

Concept used: 1) Common difference (d) = a₂ - a₁

2) aₙ = a + (n - 1)d

where aₙ = nth term or last term of an AP

a = first term of AP

n = Number of terms of AP

d = Common difference

Given question: If -22 is the nth term of arithmetic progression 5, 2, -1, ... , then n = ____ .

Solution: Given AP: 5, 2, -1, ...

First term (a) = 5

Common difference (d) = a₂ - a₁ = 2 - 5 = -3

nth term = -22

n = ?

We know that, aₙ = a + (n - 1)d

Substituting the values, we get,

-22 = 5 + (n - 1)-3

-22 - 5 = -3n + 3

-27 = -3n + 3

3n = 3 + 27

3n = 30

n = 30 ÷ 3

n = 10

∴ If -22 is the nth term of arithmetic progression 5, 2, -1, ... , then n = 10.