Question

19th term is 52 and 38th term is 128 find the sum of first 56 terms

Answer 1

Sum of first 56 terms of AP is 5040.

• 19th term of an AP is given as 52.

$t_{19} = a + 18d$ = 52   .....(Equation 1)

• 38th term is given as 128.

$t_{38} = a + 37d$ = 128 .....(Equation 2)

• Now we have to find the sum of first 56 terms of AP.
• Sum of n terms of AP is given by,

$S_n$ = $\frac{n}{2}(2a + (n-1)d)$

$S_56$ = $\frac{56}{2}(2a + (55)d)$

$S_56$ = $\frac{56}{2}(a + a + (18)d + 37d)$

But a+18d is given as 52  .....(From equation 1)

and a + 37d[/tex] = 128   .....(From equation 2)

$S_56$ = $\frac{56}{2}(52 +128)$

$S_56$ = 28 × 180

$S_13$ = 5040