the sum of 5th term and 16th term of an arithmetic sequence is 50. Find the sum of the first 20 terms
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Answer:
Step-by-step explanation:
nth term of AP is given as tₙ = a + (n-1)d
5th term, t₅ = a + 4d
16th term t₁₆ = a + 15d
given,
t₅ + t₁₆ = 50
=> a + 4d + a + 15d = 50
=> 2a + 19d = 50 ------------- (1)
Sum to n terms of AP, Sₙ = n/2[ 2a + (n-1)d]
=> S₂₀ = 20/2[ 2a + 19d]
= 10 * 50 (∵ from (1))
= 500
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