Question

An arithmetic sequence has a common difference equal to 7 and its 10th term is equal to 52. Find the 17th term

Answer 1

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FORMULA TO BE IMPLEMENTED

In an arithmetic progression

First term = a

Common Difference = d

Then

nth term of the arithmetic progression is

$= a + (n - 1)d$

GIVEN

In An arithmetic sequence -

• Common difference = 7
• 10th term = 52

TO DETERMINE

17th term of the arithmetic progression

EVALUATION

Let a be the First term of the arithmetic progression

Common Difference = d = 7

10th term

$= a + (10 - 1)d$

$= a + 9d$

$= a + 63$

So by the given condition

$a + 63 = 52$

$\implies \: a = 52 - 63$

$\implies \: a = - 11$

RESULT

So 17th term of Arithmetic Progression

$= a + (17 - 1)d$

$= a + 16d$

$= - 11 + (16 \times 7)$

$= - 11 + 112$

$= 101$

Answer 2

Answer:

ANSWER

an=a+(n−1)d

a17=a+16d

a10=a+9d

a17=7+a10

a17−a10=7

a+16d−a−9d=7

7d=7

d=1