Question

25. Find the sum of 1, 3.5, 6, 8.5, .... Upto 21
terms.
a) 546
b) 520
c) 496
d) none​

Answer 1

Given

⇒First term (a) = 1

⇒Common Difference (d) = a₂-a₁ = 3.5 - 1 = 2.5

⇒Number of term = (n) = 21

Formula

⇒Sₙ = n/2{2a+(n-1)d}

now put the value on formula

⇒S₂₁ = 21/2{2×1+ (21-1)2.5}

⇒S₂₁ = 10.5{2 + 20×2.5}

⇒S₂₁ = 10.5{2+ 50}

⇒S₂₁ = 10.5{52}

⇒S₂₁ = 546

Answer

⇒S₂₁ = 546 , option 'a' is correct

                                                                 

More Information

⇒a,b,c are in AP ; 2b = a+c , GP ; b²=ac and HP ; b = (2ac)/(a+c)

⇒AM = (a+b)/2 , G= √(ab) and H = (2ab)/(a+b)

⇒A≥G≥H        In Equality Based

Answer 2

Given :-

An AP 1,3.5,6,8.5 Upto 21 terms

To Find :-

The sum

Solution :-

Finding common difference

$\sf C.D. = a_2 - a_1$

CD = 3.5 - 1

CD = 2.5

We know that

Sₙ = n/2{2a+(n-1)d}

$\sf S_{21}=\dfrac{21}{2} \bigg(2 \times 1 + (21 - 1 )2.5\bigg)$

$\sf S_{21}= \dfrac{21}{2} \bigg(2 + (21 - 1) 2.5\bigg)$

$\sf S_{21} = \dfrac{21}{2} \bigg(2 + 20 \times 2.5\bigg)$

$\sf S_{21} = \dfrac{21}{2}\bigg(2 + 50\bigg)$

$\sf S_{21} = \dfrac{21}{2}\times 52$

$\sf S_{21} = 21 \times 26$

$\sf S_{21} = 546 \bigg\lgroup Option \; A \bigg\rgroup$