Question

sum of the first fourteen terms of an ap is 1505.its first term is 10,find the 25th term.

Answer 1

if sum of first fourteen terms of an ap is 1505
Sn=1505   n=14   a=10
Sn=n/2{2a+{n-1}d}
1505=14/2{2×10+{14-1}d}
1505=7{20+13d}
1505=140+91d
1505-140=91d
1365=91d
d=15

for25th term
a+24d
10+24×15
10+360
370. hence 25th term is 370

Answer 2

Answer:

The value of 25th term is 370.

Step-by-step explanation:

Given :  

First term,  a = 10 and S14 = 1505

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

S14 = 14/2 [2 × 10 + (14 – 1)d]

1505 = 7 [20 + 13d]

1505/7 = 20 + 13d

215 = 20 + 13d

13d = 215 – 20

13d = 195

d = 195/13

d = 15

Common Difference , d = 15

For 25th term :  

By using the formula ,an = a + (n - 1)d

a25 = a + (n – 1) d

a25 = 10 + (25 – 1) 15

a25 = 10 + 24 × 15

a25 = 10 + 360  

a25 = 370

Hence, the value of 25th term is 370.

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