Question

If the first term of an ap is 7 and 13th term is 35 find the sum of first 13 terms

Answer 1

Sum of first 13 terms of AP is 199.

• First term of an AP is given as 7.

Therefore, a = 7.

• 13th term is given as 35.

$t_{13} = a + 12d$ = 35 .....(Equation 1)

• Now we have to find the sum of first 13 terms of AP.
• Sum of n terms of AP is given by,

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

$S_13$ = $\frac{13}{2}(2a + (12)d)$

$S_13$ = $\frac{13}{2}(a + a + (12)d)$

But a+12d is given as 35  .....(From equation 1)

$S_13$ = $\frac{13}{2}(a + a + (12)d)$

$S_13$ = $\frac{13}{2}(a + 35)$

First term(a) is 7.

$S_13$ = $\frac{13}{2}(7 + 35)$

$S_13$ = 21 × 13 = 199