Question

find the 16th term of an A.p 7,11,15,19 ...... find the sum of 1st 6th term​

Answer 1

$\sf{\underline{\red{\underline{\purple{Question:-}}}}}$

Find the 16th term of an A.P.

A.P = 7,11,15,19. Find the sum of first 6th term .

$\sf{\underline{\red{\underline{\purple{Given:-}}}}}$

A.P= 7, 11, 15, 19

a = 7

d = 4

$\sf{\underline{\red{\underline{\purple{To\:Find:-}}}}}$

$\sf a_{16}=?$

$\sf sum\:of\: first\:6th\:term=?$

$\sf{\underline{\red{\underline{\purple{FORMULA\:USED:-}}}}}$

$\sf{\fbox{\red{\underline{\purple{a_n= a+(n-1)d}}}}}$

$\sf{\fbox{\red{\underline{\purple{ S_n=\frac{n}{2}[2a+(n-1)d}}}}}$

$\sf{\underline{\red{\underline{\purple{Solution:-}}}}}$

$\sf → a_n=a+(n-1)d\\\sf→ a_{16}=7+(16-1)4\\\sf→ a_{16}=7+60\\\sf{\fbox{\red{\underline{\purple{a_{16}=67}}}}}$

$\sf{\underline{\red{\underline{\purple{And:-}}}}}$

$\sf→ S_n=\frac{n}{2}[2a+(n-1)d]\\\sf→ S_6= \frac{6}{2}[2×7+(6-1)4]\\\sf→ S_6=3[14+20]\\\sf{\fbox{\red{\underline{\purple{S_6= 102}}}}}$

Answer 2

Answer:

(1) 67

(2) 102

Step-by-step explanation:

16th term = a+(n-1)×d

= 7+(16-1)×4

= 7+15×4

= 7+60

= 67

sum of first 6th term is :-

sum = n/2[2a+(n-1)×d]

sum = 6/2[2×7+5×4]

sum = 3[14+20]

sum = 3×34

sum = 102