Question

Find the sum of first 20th terms of an A.P in which d=5 and 20th term is 149.Find the sum of first 20th terms of an A.P in which d=5 and 20th term is 149.

Answer 1

Question:-

Find the sum of first 20 terms of an A.P in which d=5 and 20th term is 149.

Given:-

• Common difference (d) = 5
• 20th term = 149

To find:-

Sum of first 20 terms.

Solution:-

d = 5

20th term = 149

We know,

$\sf{a_n = a + (n-1)\times d}$

= $\sf{a_{20} = a + (20 - 1) \times 5}$

=> $\sf{149 = a + 19\times5}$

=> $\sf{149 = a + 95}$

=> $\sf{a = 149 - 95}$

=> $\sf{a = 54}$

Now,

We have,

a = 54

d = 5

We know

$\sf{S_n = \dfrac{n}{2}[2a + (n-1)\times d]}$

= $\sf{S_{20} = \dfrac{20}{2}[2\times54 + (20-1)\times5]}$

= $\sf{S_{20} = 10\times[108 + 19\times 5]}$

= $\sf{S_{20} = 10\times[108 + 95]}$

= $\sf{S_{20} = 10\times 203}$

= $\sf{S_{20} = 2030}$

$\sf{\therefore Sum \:of\:first\:20\:terms\:is\:2030}$

Additional Information:-

• n = terms

• d = common difference

• a = first term

• l = last term

• $\sf{a_n = a + (n-1)\times d}$

• $\sf{S_n = \dfrac{n}{2}[2a + (n-1) \times]}$

Answer 2

here is ur answers mate..........