Question

The 6th and 11th terms of an arithmetic sequence are 38 and 73. a) Find the first term. b) Write the algebraic expression of the sequence.

Answer 1

Answer:

(a) 3

Step-by-step explanation:

6th term = a +5d. ............(1)

11th term= a +10d...…........(2)

Equating eqn 1 and 2 we get,

a+10d =73

a +5d =38

We get , d = 7 and a= 3

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

• $\sf{ a_6 = 38}$
• $\sf{ {a}_{11} = 73}$

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 = 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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