19. The Sum of first 24th terms with nth term
tn=3+2n of an AP is
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Solution:-
Given:-
=> Tₙ = 3 + 2n
To find :-
=> Sum of 24th term ( S₂₄ )
Now Take
=>Tₙ = 3 + 2n
Now Take n = 1
=> T₁ = 3 + 2 × 1
=> T₁ = 3 + 2
=> T₁ = 5
Now Take n = 2
=> T₂ = 3 + 2 × 2
=> T₂ = 3 + 4
=> T₂ = 7
Now Take n = 3
=> T₃ = 3 + 2 × 3
=> T₃ = 3 + 6
=> T₃ = 9
Now Take n = 4
=> T₄ = 3 + 2 × 4
=> T₄ = 3 + 8
=> T₄ = 11
Sequences are
=> 5 , 7 , 9 , 11 ,...................
Now we have to Find Sum of 24th term ( S₂₄ )
Formula
=> Sₙ = n/2{2a + ( n - 1 )d}
=> S₂₄ = 24/2{ 2 × 5 + ( 24 - 1 )×2}
=> S₂₄ = 12 { 10 + 23 × 2 }
=> S₂₄ = 12 { 10 + 46 }
=> S₂₄ = 12 × 56
=> S₂₄ = 672
Answer
Sum of 24th term ( S₂₄ ) = 672
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