Question

The 8th term of an AP is 37 and 18th term is 15 more than it's 12th term find the AP. Hence find the sum of first 15 terms of the AP​

Answer 1

Answer:

an=a+(n-1)d

a8=a+7d=37......equation 1

a12=a+11d

a18=15+a12

a+7d=15+a+11d

-15=a-a+11d-4d

-15=7d

d=-15/7

from equation 1

8th term =a8=a+7d=37

a+7(-15/7)=37

a-15=37

a=37+15=52

sum of first 15 terms =Sn=n/2(2a+(n-1)d)

=15/2(2×52 +(15-1)(-15/7))

=15/2(104+14(-15/7))

=15/2(104+2×-15)

=15/2(104-30)

=15/2 ×74

15×37=555

therefore, sum of 15 terms is 555

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Answer 2

Solution:-

:-Formula

=> Tₙ = a +( n - 1)d

:-Given

=> 18th term is 15 more than 12th term

:- we can write

=> a + 17d = 15 + a + 11d

=> 17d - 11d = 15

=> 6d = 15

=> d = 15/6 = 5/2

:- Now take T₈

=> a + 7d = 37

=> a + 7×5/2 = 37

=> a + 35/2 = 37

=> a = 37 - 35/2

=> a = 39/2

:- Now we have find Sum of 15 term

:- Formula

=> Sₙ= n/2(2a + (n - 1 )d

:- We have

=> a = 39/2 , d = 5/2 , n = 15

:- Put the value on formula

=> S₁₅ = 15/2(2 × 39/2 + 14× 5/2)

=> S₁₅= 15/2 ( 39 + 35 )

=> S₁₅ = 15/2 × 74

=> S₁₅ = 15 × 37

=> S₁₅ = 555

:- Answer

=> Sum of 15 term of ap is 555