Question

If for every n belongs to N, sum to n terms of an AP is
5n²+7n then it's 10th term is​

Answer 1

Answer:

102

Step-by-step explanation:

Given,

Sum of 'n' terms of an A.P = 5n²+7n

To Find :-

10th term of an A.P

Formula Required :-

$\bf Sum\:of\:'n'\:terms(S_n)=\dfrac{n}{2}[2a+(n-1)d]$

• a = first term
• d = common difference

Solution :-

According to question :-

$\bf 5n^2+7n=\dfrac{n}{2}[2a+(n-1)d]$

Given , 'n' belongs to every natural number

→ We can keep any natural in place of 'n'.

Taking 'n' = 1 :-

$5(1)^2+7(1)=\dfrac{1}{2}[2a+(1-1)d]$

$5+7=\dfrac{1}{2}[2a+(0)d]$

$12\times 2 = 2a$

24 = 2a

→ a = 24/2

a = 12

First term = a = 12

Putting 'n' = 2 :-

$5(2)^2+7(2)=\dfrac{2}{2}[2a+(2-1)d]$

$5(4)+14=1[2(12)+1(d)]$

$20+14=24+d$

$34-24=d$

d = 10

Common difference = d = 10

General form of a term in A.P :-

$\bf a_n=a+(n-1)d$

$\implies a_{10}=12+(10-1)10$

= 12 + (9)10

= 12 + 90

= 102

$a_{10}=102$

∴ 10th term of an A.P = 102