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Step-by-step explanation:
nth term of an AP a(n) = a + (n - 1) * d.
(i)
8th term of an AP is half its second term.
a₈ = (1/2)[a + (2 - 1) * d]
⇒ a + 7d = (1/2)[a + d]
⇒ 2(a + 7d) = a + d
⇒ 2a + 14d = a + d
⇒ a = -13d
(ii)
Given that 11th term exceeds one-third of its fourth term by 1.
a₁₁ = (1/3)a₄ + 1
⇒ a + (11 - 1) * d = (1/3)[a + (4 - 1) * d] + 1
⇒ a + 10d = (1/3)[a + 3d] + 1
⇒ 3(a + 10d) = a + 3d + 3
⇒ 3a + 30d = a + 3d + 3
⇒ 2a + 27d = 3
Substitute (i) in (ii), we get
2a + 27d = 3
2(-13d) + 27d = 3
-26d + 27d = 3
d = 3
Substitute d = 3 in (i), we get
⇒ a = -13d
= -13(3)
= -39.
15th term of the AP:
= a + 14d
= -39 + 14(3)
= -39 + 42
= 3.
Hope it helps!
siddhartharao77:
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Haye ni tainu happy birthday ni
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Keh ke denna
Suit tainu patiala shahi sohniye le kay dena
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Koi surprise ja gift den da idea bada purana
Fir mood banaya das deya tainu leh kithe janna
Haye tainu dinner karun vehle . Ni 5 tara hotel ch
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Beh ke denne denna denna ...
Suit tainu patiala shahi sohniye le kay dena
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Fir tere es desi jatt ne dil da shaunk pagauna
Mein rajj ke nachna naal tere appa jaddo floor te auna
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