Question

for an arithmetic progression T7=18 ,T18=7, find T101​

Answer 1

Answer:

t₁₀₁ = -76  

Step-by-step explanation:

t₇ = 18, t₁₈ = 7

tₙ = a + (n - 1)d

t₇ = a + 6d

t₁₈ = a + 17d

subtract t₇ and t₁₈

a + 6d - (a + 17d) = 18 - 7

a + 6d - a - 17d = 11

-11d = 11

∴d = -1

substitute d = -1 in t₇

t₇ = a + 6d

18 = a - 6

⇒ a = 18 + 6 = 24

   a = 24

t₁₀₁ = a + 100d

     = 24 + 100(-1)

     = 24 - 100

t₁₀₁ = -76  

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