Question

THE sixth and eleventh term terms of an arithmetic sequance are 38 and 73 find the first term write algebraic expression of the sequance​

Answer 1

Step-by-step explanation:

Given: 6th term A6= 20, 11th term A11=30

we have, An= A1+(n-1)d

=> A6=A1+(6–1)d

=> 20=A1+5d ——equation (1)

A11=A1+(11–1)d

=> 30=A1+(11–1)d

=> 30= A1+10d,equation (2)

equating 1 and 2, we have

=> d=2, substitute in eq(1)

=> 20= A1+5(2)

=>A1=20–10=10

Hence, the first term A1=10 and common difference d=2.

Hope its help..

Answer 2

GIVEN:

6th term of an arithmetic sequence is 38.

11th term of an arithmetic sequence is 73.

TO FIND:

What is the first term ?

Write the algebraic expression of the sequence.

SOLUTION:

We have given that, the 6th and 11th terms of an arithmetic sequence are 38 and 73

\sf{ a_6 = 38}a

6

=38

\sf{ {a}_{11} = 73}a

11

=73

According to question:-

➸ a + 5d = 38....❶

➸ a = 38–5d

➸ a + 10d = 73....❷

Put the value of a from equation 1) in equation 2)

➸ 38 –5d +10d = 73

➸ 5d = 73 –38

➸ 5d = 35

➸ \sf{ d = \cancel\dfrac{35}{5}}d=

5

35

✬ d = 7 ✬

Put the value of d in equation 1)

➸ a + 5(7) = 38

➸ a + 35 = 38

➸ a = 38 –35

⠀⠀⠀❛ a = 3 ❜

First term = 3

The arithmetic sequence is:-

◇ a = 3

◇ a + d = 3 + 7 = 10

◇ a + 2d = 3 + 14 = 17

◇ a + 3d = 3 + 21 = 24

⠀⠀【3, 10, 17, 24....】

❝ Hence, the first term of an arithmetic sequence is 3 and the arithmetic sequence is 3, 10, 17, 24.

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