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# Find the A.P. Whose Fourth Term is 9 and the Sum of Its Sixth Term and Thirteenth Term is 40. - Mathematics

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ConceptSum of First n Terms of an AP

#### Question

Find the A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.

#### Solution

Let the first term be a and the common difference be d

It is given that a4 = 9 and a6 + a13 = 40.

a4 = 9

rArr a+(4-1)d=9             a_n=a+(n-1)d

rArr a+3d=9

a_6+a_13=9

rArr {a+(6-1)d}+{a+(13-1)d}=40

rArr {a+5d}+{a+12d}=40

rArr 2a+17d=40

From (1):

a = 9 − 3d

Substituting the value of a in (2):

2 (9 − 3d) + 17d = 40

⇒ 18 + 11d = 40

⇒ 11d = 22

⇒ d = 2

∴ a = 9 − 3 × 2 = 3

Thus, the given A.P. is aa + da + 2…, where a = 3 and d = 2.

Thus, the A.P. is 3, 5, 7, 9 …

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Solution Find the A.P. Whose Fourth Term is 9 and the Sum of Its Sixth Term and Thirteenth Term is 40. Concept: Sum of First n Terms of an AP.
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