in an ap the 4th and the 6th term are 8and 14find the sum of first 20term
Answers
GIVEN :–
• 4th term of A.P. = 8
• 6th term of A.P. = 14
TO FIND :–
• Sum of first 20term = ?
SOLUTION :–
• If 'a' is first term and 'd' is Common difference , then nth term –
• According to the first condition –
• According to the second condition –
• Using eq.(1) –
• Put the value of 'd' in eq.(1) –
• We know that sum of n terms –
• So that , Sum of first 20 terms –
a₄ = 8 and a₆ = 14
The sum of first 20 terms (S₂₀).
We know that,
★ a₄ = a + 3d = 8⠀⠀⠀⠀⠀.............(i)
★ a₆ = a + 5d = 14⠀⠀⠀⠀.............(ii)
Subtracting (i) from (ii), we get:-
⇝2d = 6
⇝d = 6/2 = 3
Substituting d = 3 in (i):-
⇝a + 3 × 3 = 8
⇝a + 9 = 8
⇝a = 8 - 9
⇝a = -1
We know that,
★ Sn = n/2{2a + (n-1)d}
⇝S₂₀ = 20/2 {2×(-1) + (20-1)3}
⇝S₂₀ = 10 (-2 + 19 × 3)
⇝S₂₀ = 10 (-2 + 57)
⇝S₂₀ = 10 × 55
⇝S₂₀ = 550