Question

The sum of the 10th term and 16th term of an arithmetic

sequence is 78. Calculate its 13th term?​

Answer 1

✬ a¹³ = 39 ✬

Step-by-step explanation:

Given:

• Sum of 10th and 16th term of an A.P is 78.

To Find:

• What is it's 13th term ?

Solution: Let a be the first term and d be the common difference of given A.P

As we know that, nth term of an A.P is given by

★ aⁿ = a + (n – 1)d ★

So, 10th term

• a¹⁰ = a + (10 – 1)d or a + 9d

and 16th term

• a¹⁶ = a + (16 – 1)d or a + 15d

A/q

• Sum of 10th and 16th term is 78.

$\implies{\rm }$ a + 9d + a + 15d = 78

$\implies{\rm }$ 2a + 24d = 78

$\implies{\rm }$ 2(a + 12d) = 78

$\implies{\rm }$ a + 12d = 78/2

$\implies{\rm }$ a + 12d = 39....(1)

[ 13th term will be given by ]

• a¹³ = a + (13 – 1)d or a + 12d

➭ From equation 1

➭ a + 12d = 39

Hence, 13th term of A.P will be 39.

Answer 2

Step-by-step explanation:

n/2(2a+9d)+n/2(2a+15d)=78

n/2(2a+9d+2a+15d)=78

n/2(4a+24d)=78

n/2(4a+24d)=78

2n/2(2a+12d)=78

n/2(2a+12d)=39

s13=39