Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Find the middle term of the A.P. 6, 13, 20, ...., 216.

Question

Find the middle term of the A.P. $6, 13, 20, ...., 216$ .

111

Views: 806 students

Found 8 tutors discussing this question

Levi Discussed

Find the middle term of the A.P.

6, 13, 20, ...., 216

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Clearly,

6, 13, 20, ....., 216

is an A.P. with first term

a = 6

and common difference

d = 7

Let there be

n

terms in the given A.P.

Then,

a_{n} = 216

⟹ a + (n + 1) d = 216

⟹ 6 + 7 (n - 1) = 216

[∵ a = 6

and

d = 7]

⟹ 7 n = 217 ⟹ n = 31

Here,

n

is odd so

(\frac{n + 1}{2})^{t h}

i.e.

(\frac{31 + 1}{2})^{t h} = 1 6^{t h}

term is the middle term and is given by

a_{16} = a + (16 - 1) d = 1 + 15 d = 6 + 15 \times 7 = 111

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes