Question

the sum of the first 10 terms of arithmetic sequence is 530. what is the first term if the last term is 80 and the common difference is 2

Answer 1

Answer:

sn=530

n=10

an=80

a1=?

Formula:

Sn=(n/2)(An+a1)

530=(10/2)(80+a1)

530=(5)(80+a1)

530=400+5a 1

530=5a1+400

5a1=130

a1=26

Answer 2

Given: The sum of the first 10 terms of an arithmetic sequence = 530

           The last term of the sequence = 80

           The common difference = 2

To find: The first term

Solution: We see, S = 530, an = 80, d = 2, n =2.

The formula of the sum of an arithmetic sequence when the first and last terms are given: S = n/2 (a1 + an)

Therefore according to the question,

530 = 10/2 (a1 + 80)

⇒ 530 = 5 (a1 + 80)

⇒ a1 + 80 = 530/5

⇒ a1 = 106 - 80

⇒ a1 = 26

Hence, the first term of the sequence is 26.

Answer: 26