Question

The first term of an arithmetic sequence is 6 and the sum of the first 6 terms is 66. a. What is its 6th term? b. What is the common difference of the sequence ? c. What are the first 6 terms of this sequence ?​

Answer 1

$\huge\boxed{\mathtt\red{SOLUTION:-}}$

Given :-

• first term of arithmetic sequence is 6
• sum of first 6 term is 66

To Find :-

1. The 6th term
2. the common difference of the sequence
3. first 6 term of the sequence

Assumption :-

✰ let a be the common difference

then, the sequence is :-

⟹ 6, 6+a, 6+2a, 6+3a, 6+4a, 6+5a

Solving :-

According to the Question :-

⟹ sum of 6 numbers = 66

✒ 6+6+a+6+2a+6+3a+6+4a+6+5a = 66

✒ 36+15a = 66

✒ 15a = 66-36

✒ a = 30/15

∴ a = 2

$\large\boxed{\mathtt\green{∴The\: common \:difference\: is\: 2}}$

Answers :-

(a). The sixth term was:-

6+5a = 6+10 = 16

∴ The 6th term of the sequence is 16

(b). ⟹ The common difference = a = 2

(c). ✮ First 6 terms of the sequence are :-

1. 6 = 6
2. 6+a = 6+2 = 8
3. 6+2a = 6+4 = 10
4. 6+3a = 6+6 = 12
5. 6+4a = 6+8 = 14
6. 6+5a = 6+10 = 16