Question

twenty third term of A. P -100, -90, -80, -70.......... ​

Answer 1

$\underline{\bf{GIVEN:-}}$

• First term(a) = -100

• Common difference(d) = -90-(-100) = 10

• Number of terms(n) = 23

$\\ \underline{\bf{TO \: FIND:-}}$

$\sf a_{23}$ = ?

$\\ \underline{\bf{SOLUTION :-}}$

⇒ $\sf a_{n}$ = a + (n-1) × d

⇒$\sf a_{23}$ = -100 + (23-1)10

⇒ $\sf a_{23}$ = -100 + (22)10

⇒ $\sf a_{23}$ = -100 + 220

⇒ $\sf a_{23}$ = 120

Therefore, twenty third term of AP is 120.

$\\ \underline{\bf{Extra \: Formulas \: of \: AP:-}}$

• Sum of n terms in AP = Sn = n/2[2a + (n − 1) × d]

• Sum of all terms in a AP with the last term as 'l' = n/2(a + l)

• General formula for AP = a, a+d, a+2d, a+3d... so on

Answer 2

A.P : -100, -90, -80, -70.....

a = -100

d = a₂ - a₁ = -90 - (-100) = -90 + 100 = 10

n = 22

a₂₂ = a + (n-1)d

a₂₂ = -100 + (22-1) 10

a₂₂ = -100 + (21) 10

a₂₂ = -100 + 210

a₂₂ = 110

twenty third term of the given ap is 110