Find the sums given below:34 + 32 + 30 + … + 10

1.	Find the sums given below:34 + 32 + 30 + … + 10
Answer» Given A.P: 34 + 32 + 30 + … + 10 a = 34; d = a₂ – a₁ = 32 – 34 = -2 and the last term l = a_n = 10 But, a_n = a + (n – 1) d ∴ 10 = 34 + (n – 1) (-2) ⇒ 10 – 34 = -2n + 2 ⇒ -2n = -24 – 2 ⇒ n = -26/-2 = 13 ∴ n = 13 Also, S_n = \(\frac{n}{2}\) (a + l) where a = 34; l = 10 S₁₃ = \(\frac{13}{2}\)(34 + 10) = \(\frac{13}{2}\) × 44 = 13 × 22 = 286

Answer»

Given A.P: 34 + 32 + 30 + … + 10

a = 34; d = a₂ – a₁ = 32 – 34 = -2 and the last term l = a_n = 10

But, a_n = a + (n – 1) d

∴ 10 = 34 + (n – 1) (-2)

⇒ 10 – 34 = -2n + 2

⇒ -2n = -24 – 2

⇒ n = -26/-2 = 13

∴ n = 13

Also, S_n = \(\frac{n}{2}\) (a + l)

where a = 34; l = 10

S₁₃ = \(\frac{13}{2}\)(34 + 10)

= \(\frac{13}{2}\) × 44

= 13 × 22

= 286

Discussion