Question

यदि एक समांतर श्रेढ़ी के प्रथम n पदों का योगफल 2n + 3n² हो तो समांतर श्रेढ़ी का xवाँ पद ज्ञात कीजिए। [संकेत: tₓ = Sₓ – S₍ₓ₋₁₎]

Answer 1

$\LARGE\underline{\underline{\sf \red{G}\blue{i}\green{v}\orange{e}\red{n}:}}$

Sum of n terms = Sn = 2n + 3n²

$\LARGE\underline{\underline{\sf \red{T}\blue{o}\:\green{F}\orange{i}\pink{n}\red{d}:}}$

Tx terms of AP ?

$\LARGE\underline{\underline{\sf \red{S}\blue{o}\green{l}\orange{u}\pink{t}\purple{i}\orange{o}\red{n}:}}$

S1 = 2(1) + 3(1)² = 5

Sum of 1st term is same as first term

so ,,

a1 = $\large\red{\boxed{\sf a=5}}$

S2 = 2(2) + 3(2)² = 4 + 12 = 16

S2 = a1 + a2

16 = 5 + a2

→ a2 = $\large\pink{\boxed{\sf a_2=11}}$

Common difference

d = a2 - a1 = 11 - 5 = 6

A.P is 5 , 11 , 17 , 23 , 29 ____________

xth term a_x = [( 5 + ( x-1)6]

⇒ 5 + 6x - 6

⇒ 6x - 1

So, Xth term of AP is = $\large\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{\boxed{\sf </strong><strong>(</strong><strong>6</strong><strong>x</strong><strong>-</strong><strong>1</strong><strong>)</strong><strong>}}$