Question

the 2nd and 45th term of an ap are 10 and 96 respectively.Find the first term and the common differenceand hence find the sum of first 15 terms

Answer 1

Heya Frnd........☺

✴ Note :- a = 1st term
d = difference


2 nd term = a + d = 10

45 th term = a + 44 d = 96

Now,

( a + 44d) - ( a + d) = 96 - 10

43 d = 86

Therefore ,

d = 86/43 = 2......... (1)

Now ,

a + d = 10

=> a = 10 - d

=> a = 10 - 2 = 8 ................ ( 2 )

Now,

Sₙ = n/2 (2a + (n-1)d)

=> 15/2 ( 2*8 + (15 - 1)2)

=> 15/2 ( 16 + 28)

=> 15/2 * 44

=> 15 * 22

=> 330 ........................( 3 )

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