Question

if the sum of the first 14 terms of an ap is 175 and its first term is -7 , find the 21st term

Answer 1

Answer:

is it 182

Step-by-step explanation:

14 term =175

1 st = -7

= -7 +175 = 185

Answer 2

$\huge {\red {ⓐⓝⓢⓦⓔⓡ }}$

Given :-

First term a = -7

Sum of 1st 14 terms = 175

To find :-

21st term

Solution :-

sum of n terms of an AP =

$</strong><strong>\frac{n}{2} (2a + (n - 1)d)$

so sum of 14 terms of an AP will be

$\frac{14}{2} (2\times - 7 + 13d)$

$\implies 175 = 7(-14+13d)$

$\implies 175 = -98 +91d)$

$\implies 175+98 = 91d$

$\implies d =273÷91$

$\implies d = 3$

Now,

Now,21st term = a+20d = -7 +20(3) = -7 + 60 = 53

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