Question

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 25th term.

Answer 1

Answer:

$t_{25} = 250$

Step-by-step explanation:

$S_{14} = 1050$

a = 10

$S_{14} = \frac{n}{2}( 2a + (n - 1) d)\\\\1050 = \frac{14}{2}( 2 * 10 + (14 - 1) d)\\\\1050 = 7[ 20 + 13d]\\\\150 = 20 + 13d\\\\13d = 150 - 20\\\\13d = 130\\\\d = 10$

$t_{25} = a + (n - 1)d\\\\t_{25} = 10 + (25 - 1)(10)\\\\t_{25} = 10 + 240\\\\t_{25} = 250$

Answer 2

Given :-

• First term (a) = 10

• n = 14

• $\rm\:s_{14}=1050$

To find :-

• The 25th term = ?

Solution :-

we know that,

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\pink{s_n=\dfrac{n}{2}\:[2a+(n-1)d]}}}}$

$\rm\longrightarrow\:1050=\cancel\dfrac{14}{2}\:[2\times{10}+(14-1)d]$

$\rm\longrightarrow\:1050=7(20+13d)$

$\rm\longrightarrow\:1050=140+91d$

$\rm\longrightarrow\:1050-140=91d$

$\rm\longrightarrow\:910=91d$

$\rm\longrightarrow\:\cancel\dfrac{910}{91}=d$

$\rm\longrightarrow\:10=d$

$\rm\longrightarrow\:d=10$

Now,

$\rm\longrightarrow\:a_{25}=10+(25-1)\times{10}$

$\rm\longrightarrow\:a_{25}=10+250-10$

$\rm\longrightarrow\:a_{25}=10+240$

$\rm\longrightarrow\:a_{25}=250$

Hence,the 25th term will be 250.

More information :-

Arithmetic progression :- A sequence in which each term differs from its preceding terms by a constant is called an arithmetic progression.which is denoted by AP.