Question

Sum of the first 14 terms of an A.P. is 1505 and its first term is 10. Find its 25^th term.

Answer 1

Given, 

a = 10 

S₁₄ = 1505 

S₁₄ = \(\frac{n}{2}\)[2a + (n – 1) d] 

1505 = \(\frac{14}{2}\)[2(10) + (14 – 1) d] 

1505 = 7 [20 + 13d] 

215 = 20 + 13d 

13d = 215 – 20 

13d = 195 

d = 15 

Now, a₂₅ = a + (n – 1) d 

= 10 + (25 – 1) 

15 = 10 + 24 x 15 

= 10 + 360 = 370 

Hence, value of 25^th term is 370