Question

if the sum of first 10 terms of an A.P. is 385and its first term is 7, find the 25th term

Answer 1

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Answer 2

Answer : 25th term of this A. P is 175

Step-by-step explanation :

Sum of first 10 terms of an A. P = 385

First term = 7

We know that,

$\boxed \: \: \: \: \boxed{ \boxed{S_{n} = \frac{n} {2}(2a + ( n - 1) d }}$

So,

385 = 5 ( 2a + ( 10- 1)d

77 = 2a + 9d

We know that,

$\boxed { \: } \: \: \: \boxed{ \boxed {a = 7 }}$

So,

77 = 2(7)+9d

77 - 14 = 4d

63 = 9d

d = 7

So,

$\boxed{ \: } \: \boxed{ \boxed{d = 7}}$

Now,

n th term of an A. P = a + ( n - 1) d

25th term = 7 + ( 24) (7) = 175.

Therefore, 25th term is 175