Question

Find the sum of 1. 5+2. 5+…………50. 5​

Answer 1

Answer:

1300

Step-by-step explanation:

n=50

a=1.5

d=1

sum=n/2(2a+(n-1)d)

sum=50/2(3+(49))

sum=25(52)

sum=1300

Hope it helps.

Answer 2

Answer :

$\large\star\:\:\:\boxed{S_{50}\:=\:1300}\:\:\:\star$

Explanation :

✧ Given :–

• A.P.  :- 1.5 , 2.5 ,3.5 , . . . , 50.5
• where a = 1.5 , d = a₂ - a₁ = 2.5 - 1.5 = 1 , aₙ = 50.5

✧ To Find :–

• Sₙ ( Sum of all the terms of this A.P. )

✧ Formulas Applied :–

$\large{\boxed{\bf{\star\: \: {a_n\:=\:a\:+\:[(\:n\:-\:1\:)\:\times\: d]}\:\: \star}}}$

$\large{\boxed{\bf{\star \:\: S_n\:=\:\dfrac{n}{2} [2a\:+\:(\:n\:-\:1\:)\:\times\:d]\: \:\star}}}$

✧ Solution :–

➪ We have, a = 1.5 , d = 1 and aₙ = 50.5

✯ Putting these values in the formula $\bf{a_n\:=\:a\:+\:[(\:n\:-\:1\:)\:\times\: d]}$.

➠ 50.5 = 1.5 + ( n - 1 ) × (1)]

➠ 50.5 - 1.5 = n - 1

➠ n - 1 = 49

➠ n = 49 + 1

➠ n = 50

➪ Now , we have a = 1.5 , d = 1 , aₙ = 50.5 and n = 50 .

✯ Putting these values in Formula $\bf{S_n\:=\:\frac{n}{2} [2a\:+\:(\:n\:-\:1\:)\:\times\:d]}$.

$\rightarrow S_{50}\:=\:\dfrac{50}{2}\:[2(1.5)\:+\:(\:50\:-\:1\:)\:\times\:(1)]$

$\rightarrow S_{50}\:=\:25\:\times\:[3\:+\:(\:49\:)\:\times\:(1)]$

$\rightarrow S_{50}\:=\:25\:\times\:(\:3\:+\:49\:)$

$\rightarrow S_{50}\:=\:25\:\times\:52$

$\rightarrow \boxed{S_{50}\:=\:1300}$

∴ The Sum of 50 Terms of the A.P. is 1300 .

__________________

➥ Additional Information :–

➧ A.P. ( Arithmetic Progression ) is a sequence of terms where after eeach term there is a common difference d .

➧ There is one more method to find the sum of n terms :-

$S_n\:=\:\frac{n}{2} \:(\:a\:+\:l\:)$      [ here l is the last term. ]

Here in this question we have : a = 1.5 , l = 50.5 and n = 50 .

$\rightarrow S_{50}\:=\:\frac{50}{2}\:\times \:(\:1.5\:+\:50.5\:)$

$\rightarrow S_{50}\:=\:\frac{50}{2}\:\times \:(\:52\:)$

$\rightarrow S_{50}\:=\:25\:\times \:52$

$\rightarrow \boxed{S_{50}\:=\:1300}$

See here the answer is the same but the formula is different . So we can use this formula to make our calculation easier.