if 19th term is 52 and 38th term is 128 in A.P. then find first 36 term sum
Answers
EXPLANATION.
19th term = 52.
38th term = 128.
As we know that,
Formula of :
General term of an A.P.
⇒ Tₙ = a + (n - 1)d.
Using this formula in the equation, we get.
⇒ T₁₉ = 52.
⇒ T₁₉ = a + (19 - 1)d.
⇒ T₁₉ = a + 18d.
⇒ a + 18d = 52. - - - - - (1).
⇒ T₃₈ = 128.
⇒ T₃₈ = a + (38 - 1)d.
⇒ T₃₈ = a + 37d.
⇒ a + 37d = 128. - - - - - (2).
From equation (!) and (2), we get.
Subtract both equations, we get.
⇒ a + 18d = 52. - - - - - (1).
⇒ a + 37d = 128. - - - - - (2).
⇒ - - -
We get,
⇒ - 19d = - 76.
⇒ 19d = 76.
⇒ d = 4.
Put the value of d = 4 in equation (1), we get.
⇒ a + 18d = 52.
⇒ a + 18(4) = 52.
⇒ a + 72 = 52.
⇒ a = 52 - 72.
⇒ a = - 20.
First term = a = - 20.
Common difference = d = b - a = 4.
To find : Sum of first 36 term.
As we know that,
Formula of :
⇒ Sₙ = n/2[2a + (n - 1)d].
Using this formula in the equation, we get.
⇒ S₃₆ = 36/2[2(-20) + (36 - 1)(4)].
⇒ S₃₆ = 18[- 40 + (35)(4)].
⇒ S₃₆ = 18[- 40 + 140].
⇒ S₃₆ = 18 x 100.
⇒ S₃₆ = 1800.