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If the 10th Term of an Ap is 52 and 17th Term is 20 More than Its 13th Term, Find the Ap - Mathematics

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Question

If the 10th  term of an AP is 52 and 17th  term is 20 more than its 13th  term, find the AP

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Solution

In the given AP, let the first term be a and the common difference be d.

Then, Tn = a + (n-1) d

Now, we have:

T 10  = a + (10 - 1) d

⇒ a +9d =52                 ...................(1)

T13 = a +(13-1) d = a +12d                ........(2)

T17 = a+ (17 -1) d = a + 16d              ..........(3)

But, it is given that T17  = 20 + T13

i.e .,  a+ 16d = 20 + a + 12d

⇒ 4d = 20

⇒ d= 5 

On substituting d = 5 in (1), we get:

a + 9 × 5 = 52

⇒ a = 7 

Thus, a = 7 and d = 5
∴ The terms of the AP are 7,12,17,22,.........

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Chapter 11: Arithmetic Progression - Exercises 1

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R.S. Aggarwal Mathematics [English] Class 10
Chapter 11 Arithmetic Progression
Exercises 1 | Q 16

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