In an AP,sum of first 8 terms is 136 and that of 15 terms is 465. Find the sum of 25 terms.​

Question

In an AP,sum of first 8 terms is 136 and that of 15 terms is 465. Find the sum of 25 terms.​

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1 month 2021-10-27T02:42:11+00:00 2 Answers 0 views 0

1. *۰۪۫G۪۫۰۰۪۫i۪۫۰۰۪۫v۪۫۰۰۪۫e۪۫۰۰۪۫n۪۫۰:

• Sum of first 8 terms(S8)=136
• Sum of 15 terms (S15) =465

* ۰۪۫T۪۫۰۰۪۫o۪۫۰ ۰۪۫F۪۫۰۰۪۫i۪۫۰۰۪۫n۪۫۰۰۪۫d۪۫۰:

• Sum of 25 terms(S25) =?

* ۰۪۫S۪۫۰۰۪۫o۪۫۰۰۪۫l۪۫۰۰۪۫u۪۫۰۰۪۫t۪۫۰۰۪۫i۪۫۰۰۪۫o۪۫۰۰۪۫n۪۫۰

Formula for sum of an A. P :

_____________

Now to find the sum of first 8 terms,

By Using formula,

S8=8/2[2a+(81) d]

136=4[2a+7d]

136/4=2a+7d

34=2a+7d

→2a+7d=34......................(1)

Now to find the Sum of 15 terms,

By using formula,

S15=15/2[2a+(151) d]

465=15/2[2a+14d]

465×2/15=2a+14d

31×2=2a+14d

62=2a+14d

62=2(a+7d)

62/2=a+7d

31=a+7d

→a+7d=31........................(2)

Subtracting equation (2) From (1) we get,

a=3

Now Substituting the value of a in (2)

3+7d=31

7d=313

7d=28

d=28/7

→d=4

Now, Let’s find the Sum of 25 terms.

By using formula,

S25=25/2[2×3+(251) 4

=25/2[6+24×4]

=25/2[6+96]

=25/2×102

=25×51

=1275

Therefore,Thesumof25termsis1275.

2. Solution :

Using formula of the sum of an A.P;

• a is the first term
• d is the common difference
• n is the term of an A.P.

A/q

&

From equation (2),we get;

∴Putting the value of a in equation (1),we get;

∴Putting the value of d in equation (3),we get;

Now;

Thus;

The sum of 25 terms will be 1275 .