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

Step-by-step explanation:

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Answer 2

Given:-

• 6th term of an arithmetic sequence is 38.
• 11th term of an arithmetic sequence is 73.

To find:-

• Find the first term and the algebraic expression of the sequence.?

Solutions:-

We have given that;

6th term of an arithmetic sequence is 38.

• a6 = 38

=> a6 = a + (6 - 1)d

=> 38 = a + 5d ........(i).

11th term of an arithmetic sequence is 73.

• a11 = 73

=> a11 = a + (11 - 1)d

=> 73 = a + 10d .....(ii).

Now, Subtracting Eq. (ii) and (i) we get,

${a} \: + \: {10d} \: \: = \: \: {73} \\ {a} \: + \: {5d} \: \: = \: \: {38} \\ \underline{ - \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: = \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: {5d} \: \: \: \: \: \: \: \: = \: \: \: {35}$

=> d = 35/5

=> d = 7

Now, putting the value of d in Eq. (i).

=> a + 5d = 38

=> a + 5(7) = 38

=> a + 35 = 38

=> a = 38 - 35

=> a = 3

• First term = 3
• Common difference = 7

So, the arithmetic sequence is ;-

• a = 3
• a + d = 3 + 7 = 10
• a + 2d = 3 + 2(7) = 3 + 14 = 17
• a + 3d = 3 + 3(7) = 3 + 21 = 24

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