Question

the sum of the 20th term and 16th term of an arithmetic sequence is 78.calculate its13th term?
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Answer 1

Sum of 20th term and 16th term = 78

Calculate = 13 th term.

→ ᵃ20= + ᵃ16=78

→ a+19d+a+15d=78

→ 2a+34d=78

→ 2(a+17d)=78

→ a+17d=78/2=39

→ a+17d=39

Hence,

13th term will be 39.

Answer 2

Answer:

Step-by-step explanation:

Let the first term be a and common difference be d

20th term = a+19d

16th term = a+15d

Sum = a+15d+a+19d = 2a+34d

2a+34d = 78

2(a+17d) = 78

a+17d = 39

18 th term = 39

20th term = 39 + 2d

16th term = 39 - 2d

13th term = 39 - 5d

13th term = a+12d

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10th term = a+9d

16th term = a+15d

Sum = a+15d+a+9d = 2a+24d

2a+24d = 78

2(a+12d) = 78

a+12d = 39

13 th term = 39