Question

3.The sum of sixth and tenth term of an arithmetic sequence is 66. 1) Find the sum of first and fifteenth term of the sequece. 2)Find the sum of 15 terms of the sequence 3) What is its eighth term ?​

Answer 1

Answer:

the sixth sense is an automatically generated sense

Answer 2

Given :-

The sum of sixth and tenth term of an arithmetic sequence is 66

To Find :-

1) Find the sum of the first and fifteenth term of the sequence. 2)Find the sum of 15 terms of the sequence 3) What is its eighth term?​

Solution :-

Step - 1

aₙ = a + (n - 1)d

From 6th term

a₆ = a + (6 - 1)d

a₆ = a + 5d

For 10th term

a₁₀ = a + (10 - 1)d

a₁₀ = a + 9d

Step - 2

Equation formed is

a + 5d + a + 9d = 66

2a + 14d = 66 (i)

Part - 1

Sum of first and fifteenth term

a₁ = a

a₁₅ = a + (15 - 1)d

a₁₅ = a + 14d

a + a + 14

2a + 14

66

Part 2

Sₙ = n/2[2a + (n - 1)d]

S₁₅ = 15/2[2a + (15 - 1)d]

S₁₅ = 7.5[2a + 14d]

S₁₅ = 7.5[66]

S₁₅ = 495

Part - 3

2a + 14d = 66 (i)

2a + 14d/2 =  66/2

a + 7d = 33

Also,

a₈ = a + (8 - 1)d

a₈ = a + 7d

a₈ = 33