Question

In an arithmetic sequence sum of first 6 terms is 120.

a) Find the sum of 1

st term and 6

th term.

b) If the 1

st term is 10, then find the 6

th term.

c) Write the sequence​

Answer 1

Answer:-

Given:

Sum of first 6 terms in an AP is 120.

a) We know that,

S(n) = n/2 [2a + (n - 1)d]

S(6) = 6/2 (2a + (6 - 1)d]

S(6) = 3( 2a + 5d)

3(2a + 5d) = 120

(a) + (a + 5d) = 120/3

a(1) + a(6) = 40.

b) a(1) = 10

As we know that, a(1) + a(6) = 40,

Substitute the value of a(1) here.

10 + a(6) = 40

a(6) = 40 - 10

a(6) = 30.

c) We have, a = 10

a(6) = 30

a + 5d = 30

10 + 5d = 30

5d = 30 - 10

5d = 20

d = 20/5

d = 4.

We know that, general form of an AP is a,a+d,a+2d... a+(n - 1)d.

Therefore, the sequence is 10,14,18,22,26,30...