Question

the sum of theb10th term and 16th term of an arithmetic sequence is 78.calculate its 13th term? ​

Answer 1

Answer:

39

Step-by-step explanation:

nth term = a + (n - 1)d

16th term = a + 15d

10th term = a + 9d

Given, a + 15d + a + 9d = 78

2a + 24d = 78

2 (a + 12d) = 78

a + 12d = 78/2

a + 12d = 39

a + (13 - 1)d = 39

13th term = 39

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Answer 2

$\large\bf{\underline{\underline{Question}}}$

the sum of the 10th term and 16th term of an arithmetic sequence is 78.

calculate its 13th term?

$\large\bf{\underline{\underline{Given}}}$

• Sum of 10th term and 16th term = 78

$\large\bf{\underline{\underline{To\: Find}}}$

• Find the 13th term = ?

$\large\bf{\underline{\underline{Solution}}}$

→ ᵃ10+ᵃ16=78

→ a+9d+a+15d=78

→ 2a+24d=78

→ 2(a+12d)=78

→ a+12d= 78/2

→ a+12d= 39

$\large\bf{\underline{\underline{Hence}}}$

• 13th term will be = 39

$\large\bf{\underline{\underline{Shortcut}}}$

Average= sum / Number

→ 13th term = 78/2 = 34

→ 13th term = 34