Find the Arithmetic Progression if A8 Is 31 & A15 Is (16+A11)

By Team Aakash Byju's | 26th October 2022

Let, A1, A2, …., An are the terms of an arithmetic progression with a common difference d.

[{"selector":"#anim-7136d60a-fdf2-46dc-bbd9-58e933847c2a","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-f0000fa3-e6bd-460e-b527-2df4faba6c26","keyframes":{"transform":["translate3d(-96.80365%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

To find any term of an arithmetic progression we use the formula

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Thus, the terms of an arithmetic progression are

[{"selector":"#anim-5ab4223b-6e20-45a1-b153-8385aa48680a","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b082f3ad-080e-4ce0-86c4-da4824f37d85","keyframes":{"transform":["translate3d(-100%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

Given that A8 = 31 and A15 = 16 + A11, and we can write

[{"selector":"#anim-139b16a9-912d-4001-8872-92a5945a2224","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-568f6fde-f1ca-47d8-bb67-dd3af75f1caf","keyframes":{"transform":["translate3d(-100.48544%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

Thus we can state

But A15 = A1 + (15−1)d, hence A1 + 14d = 47 + 3d Substituting the value of A1, we get

[{"selector":"#anim-7485b641-038c-49e6-a3be-5c2f9cbf02e2","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-39fd7f18-c66e-4832-bcd8-3f411a05377b","keyframes":{"transform":["translate3d(-89.33601%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}]

Use the value of d in (1) to find the value of A1.

[{"selector":"#anim-a68d7d5d-79fa-4074-b8ec-f5dc98d13e3f","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-65558a87-fa0e-42ef-9e53-9d3a4e7da565","keyframes":{"transform":["translate3d(-98.33729%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] A 1 A 1 = 3 + +

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[{"selector":"#anim-83457233-44f0-4235-adb8-0e6079119288","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-36e12caf-3b3a-4524-8fe6-cd740c054df6","keyframes":{"transform":["translate3d(-157.00937%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-bca5c1eb-cd30-4766-b7b5-b4fe22b20d86","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-b7ce824e-7ab6-4789-8ae8-8f31f643149a","keyframes":{"transform":["translate3d(-157.00937%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-eed7cb72-5d58-482f-bb51-7b1bba120887","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-49612949-92d9-4ef5-b21c-d97ed1e703aa","keyframes":{"transform":["translate3d(137.10693%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-4618116f-3409-4a83-b953-ac32ddebf8f5","keyframes":{"opacity":[0,1]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] [{"selector":"#anim-ee8dfa49-af95-4a04-ac68-823a1d9a892a","keyframes":{"transform":["translate3d(127.32559%, 0px, 0)","translate3d(0px, 0px, 0)"]},"delay":0,"duration":1200,"easing":"cubic-bezier(0.2, 0.6, 0.0, 1)","fill":"both"}] Memorize These Important Formulas of Pentagonal Prism for Maths Exam Maths Concept Explained: Hexadecimal Number System and Its Uses. Download Aakash App Now

Find the Arithmetic Progression if A8 Is 31 & A15 Is (16+A11)

Let, A1, A2, …., An are the terms of an arithmetic progression with a common difference d.

To find any term of an arithmetic progression we use the formula

Thus, the terms of an arithmetic progression are

Given that A8 = 31 and A15 = 16 + A11, and we can write

Thus we can state

But A15 = A1 + (15−1)d, hence A1 + 14d = 47 + 3d Substituting the value of A1, we get

31 - 7d + 14d = 47 + 3d

=> 14d - 7d - 3d = 47 - 31

=> 4d + 16, thus d = 4

Use the value of d in (1) to find the value of A1.

Since A1 = 3 and d = 4 the arithmetic progression is

= 31 - 7(4) =>

3, 3+4, 3+ (2 4), 3+(3 4)....

= 3, 7, 11, 15, ......

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