Question

If the nth term of an ap is 3-2n find the sum of 15 terms

Answer 1

Answer:

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Answer 2

Given:

The nth term of an A.P is (3-2n)

To Find:

Sum of 15 terms

Solution:

$A_{n}$ = (3-2n)

$A_{1}$ = (3-2×1)

    = 1

$A_{2}$ = (3-2×2)

    = -1

$A_{3}$ = (3-2×3)

    = -3

So, the given A.P is 1,-1,-3,-5,.....

where, $a$ (first term) = 1 and $d$ (common difference) = -2

Now,

The sum of n terms of an A.P is

⇒$S_{n}$ = $\frac{n}{2}(2a+(n-1)d)$

⇒$S_{15}$ = $\frac{15}{2}(2+(15-1)(-2))$

⇒$S_{15}$ = $\frac{15(-13)}{2}$

⇒$S_{15}$ = -195

Hence, the sum of 15 terms is (-195).